2006 Honda Element on the fritz (help diagnose & worth repairing?)

[freshchops]

My son inherited our '06 Element as his first car.  Unfortunately, soon after, it's started to accumulate endless problems.  First a drive shaft joint casing was replaced... then an alternator.
He'd been telling me that it's "acting up" and "just not driving right", so I took it for a test drive.  I was about 2 miles from home when out of nowhere, it just shut off.  All of the power to the whole vehicle just killed, like it was turned off.  I lost power steering, brakes, everything.  Restarted it and took it straight to our mechanic.  They couldn't replicate it shutting off and couldn't diagnose why it would just shut off.  Their theory was that maybe I didn't have the ignition key in firmly.  I don't think that's likely, but we were on our way.  They did say that the engine mounts were giving out and that it would explain the extra bumpy noises.

About a week later, my son said it's just revving by itself.  I checked it out and sure enough, once you start it, it rev's high by itself.  It will rev and hold RPM's between 2-3,000.  Occasionally it will drop down to normal idle RPM's but immediately jump back up.  The check engine light is one.  I'm not betting on it, but I think that the auto-shut off might be related to current revving RPM's.

He's currently not using it and I'd prefer he doesn't because if it randomly killing all power is a thing, that could be very dangerous, especially considering his inexperience with driving.

Does the whole power shutting off - or - the revving RPM's (even when parked) w/ the transmission light on point out any particular problem's that you can point to?
He doesn't want to spend another $85 just to have the mechanic tell him he can't diagnose it or that it'll be a $2,000 repair (and maybe not worth it).

The Element has approx. 130,000 miles.  It's the FWD, automatic model.

Thanks, in advance!