For some of this, I would have to actually try it to find out; but it seems rather academic since we don't expect the processor to do anything with these until the reset routine sets these things up. That's probably why the information is hard to find.
If the NMI\ liine goes down at the same time the RST\ line does, the reset essentially clears the processor so that it won't remember the NMI\ line had been up. Since it doesn't see the falling edge, it probably won't acknowledge it. Here again however, whatever I/O IC caused the interrupt on the NMI\ line normally gets the same RST\ signal the processor does, and it will clear its own interrupt output and status. It should not be able to generate interrupts again until the reset routine sets it up to do so.
The same goes for I/O ICs that pull the IRQ\ line down. They should be
incapable of doing that from the time RST\ goes down until the reset routine (or later routine) sets them up to be able to generate interrupts under the conditions the programmer chooses. When things are set up as desired, then you do CLI (clear interrupt-disable bit) in the program. Before the first CLI, the processor is basically blind to the IRQ\ line.
A low RST\ line will keep the processor inactive indefinitely. When the line goes high, the reset vector is fetched and the reset routine is begun.
Without researching it, I really don't know where BRK ranks relative to IRQ. I have never used BRK except in school in 1982. It mainly had its usage in patching PROMs and it outlived its original purpose; but then some programmers started using it in multitasking OSs, but the 6502 is not very good at multitasking anyway. I've done a lot of real-time work with a sytem of multiple prioritized interrupts and alarms to carry out scheduled tasks, with interval lengths ranging from nine microseconds to fifteen minutes. These have an effect of multitasking except with much better control of timing than a multitasking OS can give you. I never, ever use BRK though. [
Edit, 5/15/14: I posted an article on simple methods of doing multitasking without a multitasking OS, at
http://wilsonminesco.com/multitask/index.html.]