You wouldn't be making a matrix per se, the data structures from Basic don't exist in Axe. You can however kind of mimic one by having a bunch of data and treating it as a two-dimensional array like this, just use your own numbers/sprites/etc.

It depends. Do you want to have external levels, with different maps etc?  Or do you want to have it hard-coded in to the program?
Appvars are easily made, deleted etc and are good for external levels, but you'll have to get the pointer yourself with GetCalc() and manage it (which honestly isn't very much )
If you want to have it as something built into the game itself you can make the program, then recall the source of the exported program into your own source (2nd > Rcl > find the unarchived program in the menu).

that's definitely possible =)
you'll have to export them as axe source programs, edit the programs so that the data pointers (gdb<whatever>) aren't all the same, and then include a call to them (pgrmBLAH) somewhere in your main source program.