Why do we have sharps and flats when we could have indicated these notes with different letters? So obviously, we've developed theory and notation around this and it seems to work quite well, but why couldnt we developed a system for twelve letter notes ... A-B-C-D-E-F-G-H-I-J-K-L?
It's basically just the way it happened historically - we came up with the idea of a 7-note scale being something that sounded good before we came up with the idea of all possible 7-note scales living within a 12-note 'super-scale'.
Is music theory easier/more practical under 7 letter notes as opposed to 12 or something? Does it have a practical usage with scales, or 3rds and 5ths or whatever?
It can make things easier when you're dealing with pieces of music that actually stick rigidly to the 7-note scale. But once you move away from that 7-note scale in your composition, of course the presumption of a 7-note scale just makes things more awkward.
I dont like this C- sharp/flat nonsense.
Neither do I, and when I make or play music, I don't think about note names or sharps and flats at all - I don't find it useful. The only time I use those terms is when I'm talking to someone else about music because, for historical reasons, it has become 'the common language' of music. In this sense, it's a bit like a natural language (like English) - it isn't necessarily the only logical way to express ideas - it's just one way to express ideas that has evolved through various accidents of history.
You could try the fully 12-note world, and see if you like it: get hold of an isomorphic keyboard*, such as this one...
and try playing some music notated on a chromatic staff.
*though actually, this keyboard is still coloured according to the C major scale.