Yes, jets can fire bullets. There's no reason they wouldn't be able to. Almost all US fighters carry guns. Most carry the M61 Vulcan gatling cannon firing 20mm rounds. The exceptions are the F-35 series. The F-35A, used by the Air Force, carries a GAU-12 Equalizer gatling cannon firing 25mm rounds; the F-35B (the STOVL variant used by the Marine Corps) and the F-35C (used by the Navy) do not carry guns. Guns on fighters have basically the same level of utility as bayonets on assault rifles; that is, not very much.
It's not as important anymore, but pretty much every fighter jet still has a a gun or can carry one on a mount, yes. (commonly 20mm cannon of some kind)
Can jets even fire bullets? I'm no expert in physics, but somehow I think firing a bullet from a jet just wouldn't work.