The power windows stoped working and the radio wont shut off

Check the fuses. Sounds like one or two got fried during the radio install. Use test light to test all the small fuses with ignition on

In Cadillacs ( I have an Eldorado ) the radio and power to things like your windows and power trunk release, will stay on for up to 15 minutes after the engine is shut off and the keys are removed. However once you open your car door it should it should break the connection and shut the power off to your radio and windows, If it is not cutting off the power i would look for a connector that should be attached to the pin that controls your interior lights in the door frame. Probably a good cleaning or replacement of that switch should fix your problem. If that does not cure your problem then take it in to an auto electric shop to have them trace the wires to find out where a cuircut has been stuck (fused) in the on position.

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This is actually normal. There is a option in the menu on the dash to turn this off and on

Check the wire to the starter solenoid. It maybe broken or termination is loose.

there could be a wire disconnected from the switch to the windows

there is a connection that goes into the back of the radio the connection might not be fitting right so you may have to get a new 1 take out the radio and look at the connection then you will find out if it is the connection

New vehicles now have a CPU that controls everything. Removing a component like the radio will result in a confusing side effect of another.
If you put an after market radio in it's place it might not reconnect all the components needed for the CPU. You need to ask if there is a installation kit that goes with your specific make, model of vehicle when installing a aftermarket radio.

check for a good ground connection

Try a window ,see if they still work too . RAP relay supply's power for radio windows etc. when key is turned off for ten mins or till a door is open .

Check the wiring of the car and connection there may be defective or cut wire in the wiring check the voltage.......................