You can buy a volt/ohm meter that would be good enough for what you need, for not much money. You aren't testing computer circuits where you need accuracy down to .001 ohms. At work I have one like that and it was over $300 (also does Hertz, amps, etc), however I need one like that for working on newer vehicles. For circuits on "our cars", a $25 one would work just fine.
The power on the black wire with the 3-pin unplugged is odd. The black wire is ground and should have no voltage. Give the ground connections a good going over. A poor ground COULD cause feedback from other circuits. Also, one of the window motors could be partially shorted to ground internally and cause the same thing. It's hard to say anything for sure because I'm not there in person, but I'll try my best remotely! The loss of power on the red wire with the relay plugged in is odd. I'll do some thinking on that one. It does have battery voltage with the 3 pin unplugged, yes? One other possibility is somewhere the red wire is almost broken off internally. With no load, even one strand of wire will still transmit power. Put any kind of load on it and the power is gone. I got burned a couple times by that one way back when in my early auto tech days

. That's why you should always check voltage with the circuit plugged in and the load activated (except on air bag systems!), especially on higher amperage circuits.
There's a saying in the auto repair business. It goes "electricity is not an inanimate object, it is a living breathing being, and it's also a prick". Seems to be true at times.
