So I was thinking, about the next king of England, Prince Charles. When he becomes king and if he decides to name Camilla the queen consort in due time, could he decide and does he have the power and authority to grant her the crown matrimonial, thus naming her his equal and they would co-reign? If he were to die before her, could she refuse Prince William the throne until she wants to grant him it? Also, is the crown matrimonial something that even still exists.
No, impossible. There is a big difference between a queen regnant and a queen consort. Camilla can, as Maxima Zorreguita did, become queen consort. You do that by marrying a crown prince or king (Edward VIII tried that). As consort of course she'll wield huge influence on the king. All wives do.
It is impossible for Charles to appoint his wife co ruler. Parliament will never accept that. They already have some beef about her becoming queen consort, as I understand. (They probably worry about the above influence.) Let alone co-ruler or take up the throne herself, supposing Charles would die first. The rules simply don't allow for it. No matter what happens, Camilla can never ever become Camilla I of England. Not unless she commits a coupe.
Here's a nice short clip how it works: https://www.youtube.com/watch?v=BUY6HGqYweQ
The United Kingdom together with most other European monarchies are parliamentarian monarchies. What you describe comes close to an absolute monarchy. In a parliamentarian monarchy the king carries the title and little else. That 'little else' can be quite a lot, I admit. But the king needs approval for it in parliament.
Here's an example: In Belgium king Baudouin refused to countersign an abortion bill, already passed by parliament. Without his signature that bill was not valid. That could have been a real constitutional crisis. Parliament had approved. The government would have to resign. New elections. The next government would face exactly the same problem. Thus, new elections. Ad infinitum.
The solution was that the king was declared temporarily incapable of governing for 24 hours. In his absence the government became regent, and countersigned the bill. Everybody happy.
King Baudouin was very devout Roman Catholic and as such refused to countersign that bill, as the law required. His conscience wouldn't allow it. That means a different solution had to be found. This is the heaviest weapon a constitutional monarch can yield. They normally don't use it, unless it is very important, very often for themselves.
Example: Queen Juliana of the Netherlands refused to accept 'A' and 'B' princes. (That royal family breeds faster than bunnies do, they have a lot of princes/princesses not in line for the throne. The government wanted to reduce royal costs by creating 'A' princes; in line for the throne with more benefits and 'B' princes; the remainder, with less benefits.) She would rather abdicate than countersign. The government gave in. All princess and princesses receive lots of state benefits today.
They run a serious risk that the government refuses a compromise or to give in. In that case, they have to abdicate. That includes the possibility of a republic. In case no heir is available, or the heir supports the monarch.
To get back to your question; suppose Charles would insist on it? Well, he wouldn't be the first one to be mad. George III was. Parliament would not accept it. Very likely he would be declared insane, a regent appointed, end of story.
I stressed the countersign, because kings and queens do no longer sign laws first. The government does. Only then they countersign that law, and after their signature the bill becomes law.