Firstly i would like to know if the old type arcade games are written in a sort of assembly

If all you have is the ROM, then the source language is irrelevant!

Where would one find compilers for such code?
That would depend on the processor.

What instruction set do you use?
The instruction set of the processor on the board would be a good one! ;-)

Note that some old games may well be purely hardware implementations, or may use their own, proprietary, processor.

How do one get so much gaming info ( Graphics and sound ) In such a small file?
The old arcase games were pretty crude - for this very reason!

Would one be able to use the 80xx instruction set to program a game that will run on a PC emulator?
If you want it to run on a PC, why not write native x86 code?