A kohein gets preference in:
"open first" - in Torah reading or any matter of honor.
"bless first"- he gets first grabs at a zimun (alt- to make hamotzi)
"to take a nice portion first"
On the last example the Ran in Nedarim (62b) as well as Rashi in Gittin explain the case as splitting equal portions with a yisrael, where the kohen's choice is more of a subjectively nicer portion.
We see that a kohen cannot undermine another's rights. If they're rights are equal, preference goes to the kohen. So to answer your questions:
- No, he can't cut the line.
- In theory, yes (also see Pri Megadim (Eshel Avraham) O.C. 53:14), but communities are allowed to override that rule when establishing a shul.
- Sounds strange, but I don't have a source.
An interesting version of #2: Since a Kohen has rights to the first honor, but not all the honor, if mincha and maarivv were davened in one shot, does the yisrael get to lead maariv?