Okay, so...is it possible to equip one of you followers with a different weapon then they normally use. As in, if I give Boone a power fist, will he use that instead of his machete, or if I give him a shotgun will he use that and not his sniper rifle in close combat situations?

If they consider it better then there default weapon and you provide ammo, yes they will. Gun using companions are quite fond of All-American, enough they'll take the weapon from the ground without being told.

Also keep in mind that when you switch them between 'ranged' and 'melee', the script command that is doing this does not persist between game sessions, but reverts to DEFAULT, which allows both. Sometimes, FT and loading into other cells it will also lose the script setting and revert to DEFAULT, because this is what the AI packages are set to.

IIRC the only one with melee as default is Veronica.