It is quite unlikely so maybe first lets change something harmless like patching with just rotation patch or slightly change kernel configuration (like disabling Magic SysRq key in Kernel hacking section) and see if the stability is gone. if not then add various combinations of other patches. Either it remains stable (compiler bug or faulty ram in not changed code) or specific patch breaks it (code bug) it or it will be random (faulty RAM somewhere in changed code?).
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No. Some memtester that could be run from userspace is mentioned in the wifi memory corruption bug page. However if faulty bit(s) is only in the place where kernel code resides one would need to boot custom code to test it or maybe hack the kernel to uncompress itself into different RAM space and then test it from userspace.