1 to 4 are the same: They refer to time.
“Longer” applies to physical length or time; whereas “More” usually refers to quantity, so “Longer” is better.
They all refer to some period of time: “than two weeks”. When using “any longer” or “any more” there is no need to specify “than…”; it is implied. Whereas without “any”, “longer” or “more” should be followed by “than…”.
5, Is a different question “Will you still stay even though…” some other factor applies “… your are sick”; “…the weather is bad” “. . the show is over”.