To get all the way to India would take several steps. At the turn of the century there were three cables from Aden to Bombay. So, if you needed to wire Madras from London, the message would first have to be sent to Aden, then to Bombay, then on to Madras.
In general, most of the long line pre-WW2 cables were single conductor only (one channel). Here is a typical design:
So, a message can only be sent in one direction at a given time. The telegraph operators had conventions for negotiating the exchange. For example, if an operator had no more words to send he might signal NM, meaning "no more". To tell the other operator you are ready to receive you could send GA (go ahead). Duplex or quadraplex systems were more common on land.
Damage to cables was (and is) a constant problem. Usually the damage is accidental and is caused by a trawler or by a ship anchor. The cables are designed to be very tough, so it is hard to break them, even for a big ship. Shifting sands often bury cables, so in many cases you cannot even tell that they are there.
If a cable is damaged, then a cable ship goes out to repair it. It uses a special hook to grab it and drag it to the surface. Cable ships have special equipment for testing cables. How long it would take to repair a line depends on a lot of different factors, so it might be a few days or few weeks.
In many cases the government and the military, in particular, would have priority over transmissions. Telegraph cables have almost always been commercial ventures, though, so the government had to pay just like everybody else.