There are no good ways to diagnose crashes in general. The raid equipment corruption bug is sufficiently understood that it can usually be identified. Other crash causes are usually not sufficiently understood to have reliable methods of identifying them.
A crashing save on DFFD may allow someone to identify the cause, if it's consistent (and "random intervals" doesn't sound consistent).
The 32 bit version can run out of memory if the game memory footprint exceeds 2 GB.
If you're using TwbT you may try to disable it and see if it help. It has been a crasher in the past, although it currently mostly cause crashes right on embark but not afterwards.
Note that a bugged save ought to be supplemented with needed info about OS (and version), DF version (not only version number, but also 32/64 bits, legacy, etc.). Tools/utilities are important, and omitting to mention mods borders on the criminal.
If the cause of the crashes can be identified it varies if it can be fixed. Sometimes a bugged creature can be killed, but many crash bugs don't have any known fixes. Retire/reclaim is a big hammer that sometimes work, at the substantial cost of having to repair the damage caused (stockpile contents spread all over the place, booze lost, prisoners released [kill those before retiring!], and other issues).