Yes, they all have blood, but not intense gore (shooting off heads, mutilation of body parts, etc.)If you are looking for gore, then have a look at Call of Duty, especially if you want a decent melee...
You can in HALO 1 if you use mods, but it has to be on the computer.
No, not without mods.
No there isn't which is a bit of bad luck as it would be good if there was