Mannerisms:
Show the use of all senses. Humans mostly rely on vision. As a felar all of your senses are keener, so perk your ears when you listen and sniff at new things you see.
For cats, touch is a sign of great trust. Only ever use close-contact socials on someone you consider a close friend. If a stranger pats you on your head, offers you a hand or someshit, hiss at them. Don't speak of it; it shouldn't be a conscious thought for your character.
Remember that cats like to be clean, so your character might spend time grooming or picking out fleas. Use socials like pawpreen or groom, or some custom emote.
You have claws, incorporate them in your emotes as well.
Be bad at hiding your emotions -- your tail and ears will betray you if you're anxious or overjoyed. Stoic, emotionless felar are nonsense! Well, unless you truly don't feel anything (perhaps assassins get an excuse when in martial trance).
Generally, you are a being of instinct. If you are chaotic, be impulsive. If you are orderly, then be hidebound. Either way, careful analysis is not the first thing you do when solving problems.

Speech:
Pronouns are typically not used in felar language, so unless you are roleplaying a very educated felar who speaks common extremely well, don't use them. This includes speaking of yourself (use your name instead) and inventing nicknames if you don't "know" someone else's proper name.
Intersperse your speech with cat sounds (hiss, purr or even meow). Especially if you are anxious or worried.
Optionally, use words from the felar vocabulary found in the lyceum. I recommend only doing that sparingly, though.

Society:
See the helpfile. It explains quite nicely why felar are not suited for religion and why they mostly don't trust magic. Otherwise, you fit quite well anywhere, it's going to depend on your character's upbringing too much for me to be able to give any coherent advice.

Other:
Be lazy. Cats, like all predators, are lazy.
Be curious. That proverb about cats and curiosity exists for a reason.
For laughs, when you get out of water, vigorously shake yourself dry, incidentally showering everyone nearby.