The lights going out and coming on again sounds like an auto reset circuit breaker. Usually Ford RVs have a fuse/relay box under the hood for all chassis functions, although sometimes found under the dash.
On the lighters, unplug the wire from the back of the dash for the one you shorted out by dropping something in it. If they weren't factory installed, there may be an in-line fuse in the wiring, you'll have to trace it back to where it's connected to 12 v(+).
Gulf Stream usually wired the dash radio to work from chassis or house batteries by way of a dashboard switch, might be labeled by a music note. If so equipped, try the radio after switching to other source. It's failure might be the result of the other issues you report.