Is there a way to "fake" a cpu, say a 68060 through fpga (or whatever its called) and stick it on a new design pcb to make a cheap accelerator?
Yes, in principle. Note that for instance the Minimig emulates a 68000 core (IIRC).
Is it possible to use old Pentium II chips in some way for cheap accelerator cards?
In principle you could do, but you'd probably be better off using a cheap and plentiful ARM or MIPS cpu, which would use significantly less power and be a great deal more capable.
IIRC once upon a time there was (or was planned), some sort of Amiga accelerator which uses the CPU power etc.. of a PC to help accelerate the Amiga. I may be wrong.
There were bridge boards for big box amigas that had x86 cpus on them, hellishly expensive mind, but apparently quite usable. Is that what you mean?