I have Terraria on steam and I wish to play tremor mod with my friend on host & play, so my question is:
Can I use mods on Terraria without getting banned on steam or lose my terraria account?
The Terraria modding community is well-established. You won't lose your account for using (non-cheating) mods in Terraria.
Terraria has no anti-cheat features, nor even have accounts.
Steam will not care/detect whether you cheated or not.
Terraria doesn't even have accounts for you to get banned with.
There are zero risks.
I've backed-up my save game to clone items and materials plenty of times.