However, I suspect that you might have a faulty install, and something has happened to the keyplants. At least, I can't think of another reason for the "B" key not to work if the keyboard itself is fully functional.

Sturmford is a fairly early town, and the shops in there tend to supply fairly low-level stuff. I've noticed before when playing the game that you can try and buy a particular spell, and it's never there until you actually find one in a chest somewhere. After that, you get the thing everywhere.

Re your promotion difficulties, the skill points you get are awarded but not assigned automatically. You have to do that, and it sounds as though you have not assigned them to any specific use. Double-click on one of your characters, and explore the screens brought up by the 4 tabs just to the left of the column of character portraits. You probably want the Skills screen, which IIRC is the second tab.

As to using spells, once you've got the spell-book open, try double-clicking on the icon of the spell you want to cast.