Edit: Depends on what sorts of beliefs and how it affects others. Some beliefs are toxic af, destructive, anti-social, etc and there's no choice but to judge them in order to avoid a precarious situation.
Depends on all sorts of things, like sleep amount, mood, preoccupation, etc... Sometimes both, sometimes one, sometimes the other, sometimes neither.
Are you likely to spread your melancholy mood or demeanor everywhere you go when you're in that state or keep it to yourself/for appropriate settings so people don't have to unnecessarily deal with it?
If I feel sad, I talk about it with people I’m close to. Talking can be a great source of relief. I usually do so to vent or seek advice.
However, I wouldn’t “spread” my mood in a way to purposefully bring others around me down.