The following is from Timatic, the database used by airlines:
Visa required, except for passengers with a residence permit, valid for the period of
stay, issued by Switzerland or an EEA Member
State for a maximum stay of 90 days
Visa required, except for passengers with a residence permit issued by Bulgaria,
Croatia, Cyprus or a Schengen Member State for
a maximum stay of 90 days
And for Bulgaria:
Visa required, except for passengers with a residence permit issued by Croatia,
Cyprus, Romania or a Schengen Member State for
a maximum stay of 90 days.
So yes, you can visit them all without a visa. Present your passport and residence permit card at the border
Additionally, is there any other document or anything that I must possess when traveling by air/road/rail?
I wish to enter and exit from one of these countries by air but travel between them by train or bus. Am I allowed to do so?
Will my passport be stamped in all the places upon entry and exit?
Yes, they are supposed to stamp it by law (except on exit from Serbia), but if entering Serbia by land, there's a good chance they won't bother to. If you're unlucky enough to get a lazy officer on entry but a strict one on exit, this could be a problem. So I recommend you to ask the Serbs to stamp your passport (as most Serbian border guards don't speak English, mime it with your hand while saying it)