A person who runs the instance blocks ones that may be deemed as unsafe, you can further block users and sometimes instances depending on the instance (But this will only block it for your view)
If the Instance displays it publicly than yes overwise no
Mastodon is more towards what Twitter is like, as Lemmy is more towards Reddit, Crossover for them can be done on things like Kbin/Mbin but they are confusing to begin with. If you have a certain Social Media you like we can most likely find a Fediverse version