Radio, dome light, power mirrors not working

That is correct. Fuse 17 is tied right to the battery positive terminal for constant 12 volts on the pink wire in the radio's gray connector. That is the memory wire for the station presets and clock. It is the first wire in that plug. Chrysler almost always used the interior lights fuse for the radio's memory circuit. On other car brands, you could find it tied to the horn, the brake lights, or possibly the cigarette lighter.

The wire next to the pink wire is red. That is the switched 12 volts from the ignition switch.

If you are confused because the interior lights are staying on, there is likely a door jamb switch that is out of adjustment. I can describe how to reset that if necessary.

Woah. Woah. What did I do to help solve this?

The ignition switch used on your truck, (and two of my four minivans), has caused a real lot of problems due to high current flowing through some of the contacts. This affects people much more when they use the heater fan on the higher speeds a lot and when it is on those higher speeds when the ignition switch is turned on and off. That causes a lot of arcing on two contacts. That results in resistance developing over time, and current flowing through resistance creates heat. That heat builds and builds, then migrates out to the connector terminals and burns them up too.

Check your old ignition switch to see if two terminals are black or discolored. If they are, the same thing is going to happen to your new ignition switch in short order unless you do my repair procedure that I will be happy to describe.

This part of the ignition switch runs the heater fan, radio, and power windows, (if you have them), on the same circuit. A common symptom used to be when running both power windows down at the same time, when they bottomed out, it is normal for current flow to go up a lot until you release the switches. That higher current flowing through the resistance in the switch results in a drop in voltage to that circuit, and the radio misinterprets that as you turned the ignition switch off. For that instant, if you were playing the cassette player, it will kick that out to prevent flat-spotting the rubber pinch rollers. To you that sounds like the cassette player changed direction.

If you are referring to the door jamb switch that you replaced, those are auto-adjusting, and sometimes over time they become over-adjusted, then they do not turn off when the door is closed. To reset this style, set it in a deep socket so you can tap on the terminal end. The collar supported on the end of the socket will snap down closer to the terminals. You should be able to move the switch body a good quarter inch, and maybe more. I would go as far as it will easily go. That puts it too far the other way. Reconnect it, pop it back into the body, then just close the door like normal. The switch will self-adjust by itself. The first click spreads the fingers on the collar to hold it in place. As the door goes beyond fully-closed and compresses the rubber weatherstrip, the switch will adjust in a little more, but it will still be okay. The weatherstrip pushes the door back out once it is latched, but just a little.

If you find that switch over-adjusts too often, spread a little black RTV gasket sealer on the ridges, then pop it into the body. Close the door like normal to be sure the switch self-adjusts in far enough. If you are too gentle, it will not go in far enough, then, when you really slam the door, it will break that bond.