When I try to compile a program with Axe 1.2.1 on the Nspire 84 emu, it gives me a messed up break screen, I have to replace batteries, and it reboots twice. Can I fix this?

Chances are the emulator doesn't properly emulate the flash unlock or some other fancy stuff Axe needs. TI's 84+ emulator for the Nspire isn't very good.

You would have to ask Runer112. Quigibo intended to keep Axe Nspire compatible before but I am unsure if Runer112 continued that route.

The compiled programs themselves are compatible. But with how complicated the compiling process has become, I'm not sure that compatibility can be retained for the application itself. But I'll keep it in mind.

Axe uses neither of those. My money's on the flash unlock as the issue. And there isn't really any way around a hacky flash unlock as far as I can tell; the OS tries to stop you from unlocking flash, so you have to abuse things.

No, it's always needed. Axe uses the swap sector to store data while compiling.

I assume the swap sector was originally used to retain compatibility with 83+ and 48KB RAM 84+ calculators. It's possible that the extra RAM, if available, could be used instead of the swap sector. But coding that capability would consume code space that I don't really have to give right now to address this relatively niche compatibility problem. I'll keep it in mind down the road, though.