1. No, but it's good practice to have them.
2. If everything is connected all the time, there isn't a possibility, but many times you have to rework/debug/troubleshoot, and that's when you could accidentally leave it floating.
3. If there is enough leakage in the surrounding circuit to build up a charge on the gate that the high impedance can't bleed off.. sure it could turn them on.
4. You'd leave the top FETs to be able to float, which could turn them on in some random configuration, partially energizing the circuit... that's just a not nice, clean design.
It's best practice to tie gate to source with some large resistance. In the unlikely event that a wire comes loose, you are debugging something and leave that node disconnected, etc... you won't bias the device on with static build-up, and burn something up on accident. It's really cheap insurance, so it's done 99.9999% of the time. I suggest you just pony up the additional 4 cents and put in some little 1k pull-downs and have it over with. Better safe, than sorry... as the old adage goes.