Does Mandos have jurisdiction over men?

[Salocin]

I can think of 4: Tuor, Bilbo, Frodo, Samwise. Probably Gandalf as well

Could you please site where you heard that Tour went to the immortal lands?

Bilbo, Frodo, and Sam were hobbits, not men. There fate is never mentions. Neither is that of the Ents for that matter. They were not Children of Iluvaltar and unlike the dwarves, I do not think Eru had made any promises or plans to adopt them.

Gandalf was a Maia. He was simply desguised in human form and this would no more stop him from stepping onto the immortal lands than it would make him mortal or subject to any of the other faults men are subject to.