In respect to this, which is better Star Wars Knights of the Old Republic 1 or 2?
KOTOR 2 is a deconstruction of Star Wars, rather than an attempt to emulate its most popular traits. The difference between the two games is apparent in their basic premises. KOTOR 1 is about a galactic war you're trying to end, and KOTOR 2 doesn't even have a war.
Secondly, are KotOR 1 and 2 connected? Yeah you should play 1 first, it's brilliant. To be fair you could probably find a free or very cheap copy since it was in the $1 Humble Bundle. Play Kotor 1 first, alot of the stuff in Kotor 2 relates back to the events of Kotor 1.
Then, is KotOR 2 still worth playing?
Kotor 2 was a bit rushed out but its still a good game and worth playing. Yup. Even though it was nowhere near the quality of the first one, KotOR II was still a solid game. And if you loved the first one, you'll at least like the second one.
What happened between KotOR 1 and 2?
The Mandalorian Wars was all stuff that came before KotOR 1. The Jedi were actually quite weak during KotOR 1 and after the end of KotOR 1, the remains of the new Sith led by Darth Nihilus and Sion started to wipe out the remaining Jedi with their Sith assasins (again, this is all explained in KotOR 2).