There is a good chance the pedal is bent down from hard braking over the years. The springs on you bands may also be wean, some of the vendors had a stronger band spring which is a good thing.
Yes. And it may need to be adjusted a little tighter.
I do have one book that was written about them around about 1929 so it'll be helpful, but I'm sure I'll need more!There is a few adjustments to be made for a good neutral. If you don't have a few manuals you should buy at least the "Model T Ford Service" book as it tells everything you will need to know and also tells you how fast you can get each job done. Until you know your car don't trust the lever quadrant to hold in neutral. My father got run over when he was a kid working at a garage and cranked a T that jumped out of neutral.