According to this list, how were nobles promoted? For instance, Baron to Viscount, and Duke to Archduke? If ranks are hereditary, were there only a specific number of each rank given out in each country? Is there a record of this? For instance, does England's Parliament have a document outlining these numbers?
Firstly, there is the distinction between inherited versus conferred titles. Inherited titles passed more or less automatically from parent to child e.g. King, Duke, Baron, Viscount.
Conferred titles were granted as rewards for merit e.g. knight or as temporary offices or powers e.g. viceroy (in the stead of the king.)
Inherited titles were attached to land or very rarely some other kind of economic asset like a harbor or fishing rights. Our current use of the word "title" to mean proof of ownership comes directly from the titles of aristocrats. Just to confuse things, titles could be bought and sold, might be seized by the king because of some real or fictional offense or won or lost in battle.
Titles were so important that they became and individuals legal and cultural formal identity e.g. the Earl of Essex. All obligations of fealty, military service, taxes, protocol etc attached to the title, not the individual. Any particular individual could have a vast array of titles. In fact, one could argue that "collecting titles" was the primary occupation of nobles.
To the extent that noble titles had actual ranks, they expressed the degree of fealty, in the form of military service, the holder is required to give to another nobel, usually the king. The granting of fealty was very much a business deal and really had no defined hierarchal structure. Most nobles owed fealty and it's military service to the King, because the King was the strongest nobel around, but they might also pledge or inherit fealty to another nobel for various reasons Fealty was not alway hereditary even theory much less practice.
Since fealty really established chain of military command, ranks and deference depended on fealty instead of title. So, if a Duke also held the title of Baron of some little backwater and that that title of Baron came with an obligation of fealty to a Count, then the Duke would be obligated to follow the orders of the Count and to defer to him in matters of status and protocol... in theory. In reality, Dukes were usually richer and more powerful than Counts and the Count wouldn't bring the matter up.
Dukes held titles that in legal theory made them independent of the King but they pledge their fealty anyway...sorta, kinda, maybe on a good day. Earls, Counts and Barons started out as various Germanic military ranks with decrease grants of conquered land but by the medieval era had become all muddled and a Baron might have more land, wealth and military power than an Earl.
Secondly, as for promotions, since titles weren't really ranked, there weren't any. Most nobles lived and died with their inherited titles. The only situation analogous to promotion occurred when a King or other high noble found themselves holding titles because of conquest, treason or because a line had died out. (One of the special powers of the English crown was that titles "reverted" to the crown if there were no male heir.)
Kings could parcel out or recombine these titles and their associated lands to "create" a new title of nobility and confer that title on this or that individual.
It might look like a promotion to modern eyes to read that a the Baron Strange was created by King Henry the Nth, the Earl of Nonsuch, for services in the Third Bloody Stupid War of Godforsaken, but really he was just being paid for service in land. The individual was still Baron Strange, but now he had that nice piece of Nonsuch as well. If the title of Baron Strange owed fealty to Count of Down, then, even though the individual now also held the title of Earl, would in his persona as Baron Strange, still have to demonstrate the rituals of fealty to the Count of Down.
Still as lineages rose in power, the size of their titles usually rose and fell in tandem. That would also look somewhat like promotion and demotion to modern eyes but since titles were land and land was wealth, it was really just their bank accounts rising and falling. (Only in the later times, when noble titles began to lose their real practical power did you find ruined nobility with titles but no wealth.)
But all of this is just rule of thumb stuff. You have to remember that this was constantly evolving system that grew over the course of a thousand years and crossed over numerous political, legal and cultural lines (even in relatively isolated England.) As such the rules for handling titles were constantly in flux and depend strongly on what particular when and where you examine.
More importantly, legalism and custom were often merely fig leafs for brute force, murder and bribery. Every single "noble" title traces back to a successful act of violence. As long as titles had real economic and military force, they continued to be apportioned largely by implicit or explicit threats of violence. There never was any real system of law, as we would understand law today, controlling who had what title. Political marriages, battlefield victories and the odd poisoning or infant strangling, led to more "promotion" than any "noble" deed.
Despite all our romantic associations, at their heart, the aristocrats were never nothing but a caste of thuggish killers who trained for warfare incessantly, fought wars purely for profit and oppressed the great majority of the population cruelly. If we weren't the inheritors of centuries of pro-noble propaganda, bought and paid for by nobles, the word nobel would have connotations of "drug dealing mob thug" instead "representing highest virtue."
Until, the Glorious Revolution and the installation of William the III of Orange by parliament on the English throne, even the politics of merry old England look distinctly lawless and more like the revolving series of coups in the 3rd world today. It was not until the "commoners" finally rose up and gutted the power of the aristocracy did titles of nobility acquire some sort of moral legitimacy by modern standards.
You don't usually get promoted. You either are or you aren't. Titles are additive. So if you are the Baron of Butterscotch, and the king decides to make you the Duke of Diddlysquat, you don't stop being the Baron, you become both a Baron and a Duke.
Medieval titles of nobility are almost always associated with land. The more land, the bigger the title. In general, you get the land first, then the title after. If you were rich enough, you could become titled, just by buying enough land. Usually you would get a title from warfare. This can happen in one of three ways:
(1) Working for the king. You fight for the king. He conquers new lands. He appoints you the ruler of the new lands. You get the title associated with the new lands.
(2) Working on your own. You gather a bunch of men. You attack and conquer some land with your men. You then make a deal with the king: recognize my ownership of this land and I will pledge fealty to you. You then get a title.
(3) Inheriting the land from a previous empire. Your family owns the land from the past. A new king comes and conquers everything. You make a deal with the king same as #2. The only difference is your family already owned the land, it didn't conquer it.
To answer your final question: there are no numbers. The titles go with land, roughly in accordance to size, but also tradition. For example, one plot of land might be a "baronage", but another of exactly the same size might be a "duchy". It depends on the history of the land. Duchies were more Roman things. Earldoms were vikingish land. Baronages were continental German (like Saxons and people like that).
Note that knights are not nobles. They are the equestrian order (horse owners).
Nobles don't get promoted, they gain titles
Someone may obtain a title 'Duke of Someplace'. If he wasn't a duke before, that event might be treated like a 'promotion'. Do note that it always involves gaining that Someplace together with it - a duke doesn't get more respect than a baron because he has a fancier title; a duke gets respect because he owns a duchy and the barons don't. This also is the limit of the number of ranks. There can be no more counts than there are counties, and there can be far less as some people hold multiple counties/count titles.
You can get a title over the previous holder's cold, dead body
There are two ways to get a title - either you inherit it from the previous holder, or you take it by force and ensure that others recognize it. The second way doesn't neccesarily require the previous holder to die, but it helps if you want him to leave it that way. Both ways are really not similar to a 'promotion'. In large conquests, a winning leader might distribute large lands to his war companions which is a bit like a promotion - but only in the very rare large-scale conquests the higher titles would be distributed that way, those were the exceptional cases that most generations didn't see.
Your father might promote you
The only reasonably common 'promotion' case is the situation where father grants some of his lands and the relevant lower titles to his adult sons. Thus, the eldest son might be given some duchy or county already "in advance", and become a king some time afterwards when the inheritance happens.
I do not dispute the other answers, but I did want to point out that George Robinson, Earl de Grey, was raised to the 1st Marquis Ripon as a result of his success in negotiating the Treaty of Washington, which ended the US/British conflict over the (American) civil war.
The British were in a precarious position because of the Alabama claims. Had events turned out different, the Americans could have made a case that the British were co-belligerents with the Confederacy. The US negotiator was instructed to get Canada in recompense for the British actions, and to accept Jamaica if Britain refused to hand over Canada.
So Ripon managed to not only save Canada, but to create an Anglo-American alliance that is arguably the most successful in modern history.
This is an example of a modern (1859) "promotion" in recognition of service to the crown.
(Aside: Although I can't find the citation at the moment, it also resulted in the removal of the last unit of British troops from American soil - a clause that the British had agreed to in the Treaty of Paris, but had never actually withdrawn the troops. So in reality, the Treaty of Washington ended the American Revolutionary war and started the Anglo-American Alliance.)
(Second aside: Ripon was successful where his predecessors had failed in part because he capitalized on his Masonic ties to the US negotiators. Conspiracy nuts are now permitted to don their tinfoil hats. I on the other hand, choose to admire a skillful negotiator.)