On the old radio I bought it has wires labeled like ‘right rear’ and beside that one has ‘right common’
Same for left rear, front right and front left, beside each has a ‘common’ wire is this common wire positive or negative
Common would be negative. If a speaker is connected with the proper polarity, the speaker cone will move out. If the speaker is connected backwards, the cone will move in. If you have one speaker connected backwards (out of phase) it will cancel about 70% of the sound. Massive difference in sound quality between the three options, correct, reversed polarity, out of phase.
The capacitor on the dash speaker alters which frequency range is reduced to the speaker, probably trying to limit the bass to the small speaker. It's the cheap way of faking a crossover for the twitter/mid range separates.
If you know how to solder I would eliminate future problems by soldering the wires directly to the speaker terminals, use 16ga wire for the speakers. If you live close to the ocean, make sure you use oxygen free speaker wire. Be sure to use 60/40 rosin core solder if you decide to solder.
As far as ohms regarding speakers as mentioned above. Most car stereos will be rated at 8 ohms. Anything rated at MORE than 8ohms is entry level junk. Higher quality stereos and amps will be rated at both 8 & 4 ohms. If you run 4 ohm rated speakers on an 8 ohm stereo, it will cause the amplifier to compensate and put out about 50% more power to the speakers. There is nothing wrong with doing it this way, I have used this configuration for more than 40 years without issues, both on home systems and automotive systems.
As you start thinking specs and power ratings, don't fall for one of the biggest misconceptions that speakers need to be rated at a higher power rating than the amplifier powering them. Not true. I have been running my home speakers, rated at 150 watts with an amp that puts out 800 watts per channel, for several years. They love it. Power equates to richness/thickness of sound, WAY more than volume level, btw.
