Essentially you would have to convince holders of more than 50% of the computing power to upgrade to the new version in order to change the way it works. Most likely this wouldn't be easily possible without holding the number of coins below the original maximum.

Alternatively, various bitcoin clones could pop up, and one of them might take over the market just because it is better in some respect (e.g. more secure, faster, or easier to use). In fact there's no inherent reason there couldn't be thousands of novel currencies competing and trading against each other.

Sure you can. It just isn't very pretty. That's a major reason why governments generally like to control currency. Forking currency can be quite bad. The good news is that when one doesn't have physical currency having two different cryptographic currencies in circulation shouldn't be hard to deal with. One could even imagine software the converts between them nearly seamlessly.