TDLR: If they are free then it's good to go.
If your use of FMOD or Unity complies with it's free functionality then you're good to go. Even if you are already paying for them already for other reasons.
Essentially yes, if a plugin is free it's good to use.
Last question the "running code on their own" and "excecutes by itself" are clarifications. If it does either of those things and is premium it's not allowed.
If it does either of those things but is free, then it's okay.
The goal here is to make sure no one can make a technically superior game by bankrolling the project. If something is free and anyone can use it it's ok.
Hope that clears things up.