Are buses or mini buses allowed to park in a residential street?

-Depends on the street, depends on the size of the vehicle, depends on the local by laws.



You haven't even told us what country you're in, never mind what town.....unless prohibited by a sign then yes ( also as long as legally taxed and insured etc) where it causes parking issues then raise this with local council who can take steps to alter the situation but you will need at least a half dozen residents to complain.
It is unlikely a full size bus would park in a residential street unless the street was part of the route or the actual terminus
yes, as long as they are not causing any obstruction there is no law against it

Check if the vehicle is displaying a current tax disc
It depends on the municipality. You'll have to contact town hall and ask.