That sounds about right on the readings you got off the compressor. One side is the run winding, the other is the start winding and the single terminal is the common to both windings.

Run might be 3 or 4 ohms, start might be 6 or 7 ohms. Check across both windings and you'll get around 10 ohms.

The capacitor test went OK, but then you need to reverse your test probes and it should show the same readings. Basically your test meter is charging the capacitor. Once its charged it won't change unless the terminals shorted to each other. But if you reverse your test probes it will go through the charging part again. All this means is the capacitor should be OK.

You could just replace the relay and the compressor might work just fine. But if the compressor is locked up inside or the bearings are tight or damaged it might pull high amperage and not last to long. There is no way to know this unless you do replace the relay or if you have a hermetic compressor analyzer handy to test it with.

You could replace both the relay and the capacitor it could work just great or see reply above.

Is the compressor OK? See the reply above. It could be, but without testing it you just can't know.

The relays are crap compared to the ones they put in refrigerators 30 years ago. You are lucky to get 5 to 7 years out of the new ones. The old ones would last 15 to 20+ years.

Just make sure the terminals on the compressor aren't burnt or melted. With any kind of luck it should be OK.