Installed aftermarket radio in a 2005 dodge stratus, the gauge needles drop and the warning lights come on when I turn it on

You probably have a cold (bad) solder joint in the dash compartment that also control the radio.

warn bushes in the alternator, when the alternator warms up the bushes will come away from the pole, in turn turns the power off, just means the bushes are so warn down they heat up and the springs shrink back in and when it cools down again the bushes are connecting again till it heats up again.

Here is a list.
2005 Dodge Stratus with Infinity Radio Wire Harness Colors
Car Radio Constant 12V+ Wire: Pink
Car Radio Switched 12V+ Wire: Red/White
Car Radio Ground Wire: Black
Car Radio Illumination Dimmer Wire: Orange/Brown
Car Radio Power Antenna Trigger Wire: N/A
Car Radio Amplifier Turn On Trigger Wire: Dark Green/Red
Car Radio Amplifier Location: Amplifier is Mounted Under the Front Passenger Seat
Front Speakers Size: N/A
Front Speakers Location: N/A
Left Front Speaker Wire (+): Dark Green
Left Front Speaker Wire (-): Brown/Red
Right Front Speaker Wire (+): Violet
Right Front Speaker Wire (-): Dark Blue/Red
Rear Speakers Size: N/A
Rear Speakers Location: N/A
Left Rear Speaker Wire (+): Brown/Yellow
Left Rear Speaker Wire (-): Brown/Light Blue
Right Rear Speaker Wire (+): Dark Blue/White
Right Rear Speaker Wire (-): Dark Blue/Orange

2005 Dodge Stratus with Infinity Radio Wire Harness Colors
Car Radio Constant 12V+ Wire: Pink
Car Radio Switched 12V+ Wire: Red/White
Car Radio Ground Wire: Black
Car Radio Illumination Dimmer Wire: Orange/Brown
Car Radio Power Antenna Trigger Wire: N/A
Car Radio Amplifier Turn On Trigger Wire: Dark Green/Red
Car Radio Amplifier Location: Amplifier is Mounted Under the Front Passenger Seat
Front Speakers Size: N/A
Front Speakers Location: N/A
Left Front Speaker Wire (+): Dark Green
Left Front Speaker Wire (-): Brown/Red
Right Front Speaker Wire (+): Violet
Right Front Speaker Wire (-): Dark Blue/Red
Rear Speakers Size: N/A
Rear Speakers Location: N/A
Left Rear Speaker Wire (+): Brown/Yellow
Left Rear Speaker Wire (-): Brown/Light Blue
Right Rear Speaker Wire (+): Dark Blue/White
Right Rear Speaker Wire (-): Dark Blue/Orange

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check your fuses on driver side dash next to the door

yes but its a dealer only job as the signal that runs to the modules is encrypted to stop general mechanics like myself from repairing it .

Check for a fuse on the underhood fuse block labeled memory if its burnt there ya go. After you check that update me and we will go from

ghkghk

a bad earth on teh back of the dash somewhere ?? if you just rewire another earth to teh radio it should cure the other lights without stripping all the dash out

your battery cables and battery posts need to be cleaned. or the pattery cables need to be replaced