Does the nonce have to be a number? Since we're just trying to produce a specific hash output, couldn't the nonce also include letters or otherwise random bits?
The nonce is an arbitrary string of bits with no particular meaning. Typically they are converted into an unsigned integer for convenience. Every possible set of nonce bits has a corresponding integer in this representation.

To get letter in a nonce, you'd have to present the bits in the nonce in some encoding scheme that had some way to encode letters. There is no such scheme in common use.