The students and me / I / we saw dinosaur fossils at the museum

Answer 1

Since "the students and I" is the subject, you need the subject form of the pronoun. Think about it this way. If you got rid of "the students," would you say
me saw dinosaur bones
or
I saw dinosaur bones

The correct sentence is
The students and I saw dinosaur bones at the museum.

Note that "we" is not used.