Welcome to the forum
If it were just the key fob issue, I would recommend that you look at the solder joints on the battery retainer clip. They are known to fail and are easily repaired.
However when you mentioned the other issues, it looks like low voltage.
The cars are fly by wire, but for a few mechanical systems everything on the car is controlled and / or monitored electronically by the ECM, BCM etc via on board bus communications.
When the battery voltage drops, either because of connectivity issues at the battery terminals or usually at the engine ground strap on the left front of the engine, or just because the battery is not fully charged then the car will start and run but not all the subsystems on the car will boot up properly. And you can and generally will get a number of seemingly random issues.
For example, when you start the car, the satalite radio box does not see enough voltage to boot up properly, but the radio does. So the radio boots and does not see the satalite radio receiver box and assumes that its not available.
Since your car is an 08, it is highly likely that the battery is failed or is failing.
This spring the batteries in my 07 Sol and 08 Sky both failed. They did a soft failure, in that the cars would start and operate, but they would experience random "failures" that were attributable to the low voltage.
Check the battery first.