You absolutely do not want a page file on a ssd. Make sure that is disabled. Even in Linux, it's best to not have a swap partition, or put it on a hdd.
Why not?
The page file should go on the FASTEST drive you have. With an eye towards random performance.
On gen1 jmicron SSDs a HDD was 100x faster then the SSD in terms of random performance.
On current gen SSDs a HDD is 100x slower in random performance.
Is it also a possibility that the crashes, if ultimately due to not having a pagefile, would occur sort of randomly? Or would they be easy to correlate with the program, seeing the computer crash consistently only when you run that program? Aren't there clean-up things that can be triggered by a program and run after the program exits?
It can be either consistent and random. (I have seen both)
I have also seen it cause both computer and program crash... it really shouldn't cause the OS to crash unless something is wrong with the OS itself
Because
https://en.wikipedia.org/wiki/Memory_protection
IIRC the last OS I have had that would blue screen due to horribad upper level programs was WinXP. Off the top of my head there is Spellforce the order of dawn and titan quest... some games would manage to bluescreen it due to doing horrible things to RAM. And in the case of spellforce: the order of dawn it was solvable by increasing pagefile size. In the case of titan case the solved it in a patch.
Oh, and the first program I wrote in C++ did something very wrong with pointers and caused instant bluescreen

. Wish I had saved it or remembered how.
If windows 7 fixed ALL the faults in its memory protection mechanisms a program would only crash itself, but low level stuff like drivers could still get the OS itself.
Regardless of protections though a program can always crash itself in such a manner unless a virtual pagefile is created.
BTW, interestingly enough photoshop avoids issues from forcing pagefile access by by creating its own custom scratch file which it directly uses for things it doesn't want to "waste" ram on.