To actually answer your a bit more specifically than some other responses:

Make sure you understand the mechanics of the other 8 classes and 100+ unlocks in the game. This may mean playing a few rounds with some of the weapons that you have a hard time countering. The more you understand about the game, the better you will be at the game.

To improve your movement and "trickstabs", play in pubs really aggressively. Try and find a "higher-skilled" pub and do it there. Then after a bit of practicing, go try out a valve server and look at how much you've improved. Just a few hours of playing with an intent on improvement will show you a big difference.

To improve on chaining kills together, actively think "If I stab this guy, what will happen next?" Go through this thought for everyone in the group you want to kill, and figure out who has the best chance for you to live and get another stab. Eventually, you'll find yourself doing this automatically without much thought.

The big thing you didn't mention is your revolver aim. Practice it! Using it is much more reliable than trickstabs, and it will translate better from working on low level players to working on higher level players, including highlander people (if that option is something you're considering in the future).

All that said, it's pub spy. Just hop in a server and have fun.