Lawn mowers (both the ride-around and push types), clippers specifically meant for trimming plants, a knife, a scythe, swathers or windrowers, haybines, weed whackers, hand mowers, etc.
You don't have to but if you don't it gets untidy.
Scissors and a small ruler, cut each blade manually.
You mean the stuff that's under the snow. Good luck.
It all depends how much rain you get, some people may start mowing their lawn in early April but others not until late April, early May.