Warning! Do NOT hook up a 12V adapter to a 9V PCE! It WILL destroy your system!
You can use a MD2 adapter for it. It'll work.
No it wont, unless the polarity is wrong (which is probably what happened). The PCE like 99% of other things that run off of 5v internally, uses the ultra commoon ~7805 type linear voltage regulator. They will take anywhere from 7.5 up to 30v input. The more voltage you input, the bigger heatsink is required (as the excess wattage is transformed into heat). With the size of the heatsink in a PC Engine, you would probably be safe running up to 13-14v input. 12v is no problem. I run mine off of 12v, and the heat increase over 9v is hardly measurable.
Also, most LM7805 clones are thermal protected, so if they do overheat it will shut down. Worst thing you can do is fry the regulator. In which case its a $0.25 part.