Go for it!
More trouble than it's worth. Just grind slow, don't let it get too hot, and give it plenty of opportunity to cool.
Since you have a couple of hammers to work on, do them in rotation. Grind on one until it starts to get hot, move to the next, repeat. Each one will have a chance to cool down and not overheat.
Yes.
Start a new thread in this section with a title like "Help me identify this hammer?"