So, first. Is it possible to store data to a single nib, or nibble of data? If it is possible, how would I do so? This would be very helpful in gamemaking, with things like coins.

The answer can be found in the command list. Just like you can read from a byte address with {PTR} and store to a byte address with →{PTR}, you can read from a nibble address with nib{PTR} (really the iPart( token) and store to a nibble address with →nib{PTR}. As explained in the command list entry, nibble pointers should be multiplied by two, as there are two nibbles in a byte.

And, next. Is there a specific sprite editing tool for making files compatible with the TI-84+? If so, where can I download it? I feel like making nice title screens for games, but I don't know where to look.

For making sprites on-calc, the best tool is certainly tileIt!, a sprite and tilemap editor made especially for Axe. For making sprites off-calc, you have a couple of options. I think one of the best options for Axe is Pixelscape, an online tool also made especially for Axe and with compatibility with tileIt!.

Zeroing a matrix? easy
just do :Fill(PointerToMatrix,Width*Height,0)
That will fill the matrix with zeros.

"Matrices" in Axe generally just mean blocks of data that you treat like a matrix. There is no built-in support for matrices, but given a W*H*Z block of memory pointed to by M, it can be treated like a matrix of width W, height H, and entry size Z. An element (X,Y) can be addressed with Y*W+X*Z+M (note that order of operations in Axe is left-to-right so Y*W+X, not just X, is multiplied by Z).