make droid-dbg DROID_ARCH=armeabi -j8
is the line I'd use to compile a 'debug' version.
note that fte's makefile should have proper dependancies, so you'll only need to make clean if you change the makefile/CFLAGS.
There are a lot of warnings, yes. Generally I do all my development/testing with msvc, which simply doesn't generate those same warnings. that's my excuse and I'm sticking to it.

If you're paranoid, try adding this to the make line: CFLAGS=-fno-strict-aliasing
That should remove the bulk of the warnings by removing the point of warning about them in the first place, but it might run a little slower.
The graphical presets menu is a little pointless on android, you probably want the second or third option. the first is a little too extreme really, and is present more for the visibility than for screenshots. The last two will eat too much performance on embedded devices. Pick the third if you want it to default to vanilla-like settings.
The engine 'closing' is it crashing. Either a segfault or a sys_error. If you run logcat (from adb or a shell on the phone itself, even after it crashed) then it should show various stuff including all Sys_Print calls (including console prints and any sys_error messages).
Any segfaults should be accompanied by a register dump and a stack trace, although I've generally not found the stack trace useful for crashes in native code.
A quick overview of interesting rendering function calls:
R_RenderScene (gl_rmain.c) - sets up the projection+world matricies, frustum
Surf_DrawWorld (r_surf.c) - figures out which world surfaces/batches are visible
GLBE_DrawWorld (gl_backend.c) - does the actual rendering work.
BE_GenModelBatches (gl_alias.c) - generates batch lists from entities (non-world bsp+mdl+spr+etc) for the backend to render.
if you're getting a crash on starting a new map, then chances are its either low memory (check for Sys_Errors) or a gl/backend crash (GLBE_DrawWorld + gl_backend.c)
It could also be part of model loading, gl_rsurf.c has a function 'GLBE_GenBrushModelVBO' which is called to prepare some vbos.
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