1. Yes, Guard can fairly easily give a Tyrant a cover save. The Guard are standard infantry, meaning only the pinky toe needs to be covered to give them a cover save. If the majority of the unit is in cover, the entire squad gains the benefit. Worst case scenario is you only have 1 guard left (or started that way), so half the unit is in cover. I can't remember if that's the bare bones minimum, or if that would take it down to a 5+... either way, it's still a cover save of some sort.
Some say it's a cheesy way of giving Tyrants a cover save... I say that Guard are meant to... you know, guard the Tyrant... and you do pay a hefty price for them. One of the benefits is being able to get cover more easily.
2. No, not under current rules. Back in the day (maybe in 3rd, or the Trail Assault Rules or something) TMC's could shoot one thing and charge another - and even shoot a different unit than the squad they were with - but currently that's not the case.
3. Sure, if you like Warp Blast. If you're going for tank-hunting, yeah, it gives you a chance to pop the tank/transport then jump on the guys inside. If you're just going for extra killy in general... well, you have it. I personally like to keep my Flyrant cheap... he clocks in at just under 150. Not a bad upgrade, though.
Khira'lyth