Okay, kudo's for having the cojones to admit to this, and post it. This is going to help us all remember safety first!
I hope it goes well for you from here out.
It's possible to do with a torch, but not easy. If you have access to an oxy-acetylene torch it will be possible, but you need to keep the torch moving and remember to try and get the entire piece the same temperature...which can be difficult, but possible.
A propane torch wont get it done...
If you cant get the fire hot enough, you might consider finding a way to introduce the forced air from beneath the fire. Perhaps a metal tube or something to force air through. Most forges work in this manner.
Um...no. You have to have the hawk head glowing hot...somewhere near 1500 + or -.
While it is glowing hot, see if the magnet sticks to it, if it does, it aint hot enough. When the magnet no longer sticks to it, you have it hot enough and can let it begin to cool.
I use a mechanics magnet...the...
The annealing process depends on the metal that is used. My guess is that your hachet head is either a shallow hardening steel, or it has a cutting edge heat welded into the head. In either case I would probably bring it to non magnetic and let cool overnight in the fire a couple times.
Once you...
That really depends on the person. Most people dont have much use for a chopper unless they spend a lot of time out in the woods or around a camp.
I dont own one, but I sure could use one when I am back in the woods behind my house. ...someday.....
I have to tell ya, I admire your willingness to give it a shot. I love hawks, own a couple forged hawks, never made one but I would love to give it a shot someday. I love this idea, but right now I have to force myself to focus on what I have on my plate...which aint easy since you put this in...