Fuse #7 for stop lights
Fuse #12 for cruise control.

There is nothing common between the cruise control and the stop light circuit, so check these two fuses first. They might be the problem.
Also check the brake light bulbs. Rotate the socket back and forth a few times to try and break through any corrosion that may be between the two surfaces where the bulb holder meets the circuit board.

About the starter....
It sounds to me like the starter bendix is not releasing from the flywheel quick enough after you let off the start switch.
It uses a spring to retract the bendix gear from the flywheel teeth.

The bendix slides in and out on a shaft. If this shaft gets rusted or corroded, the bendix may not release quick enough, and it may get overdriven by the engine. This will make a sound like what you're hearing.
The contact points in the starter solenoid could also be sticking.
This can also cause the bendix to retract too slowly.
The problem may go away after you start the car a few more times.
If it doesn't, you need to get the problem resolved before you damage the gear teeth on the starter ring (flywheel).

About the check engine light.
Try removing and reconnecting the negative battery terminal.
This will reset the computer, and the light should go off.
If it re-appears, you need to read the computer codes and find out what is causing the problem.

hope this helps
steve

Edit to add:
When I use the term "Starter Bendix", I'm talking about what is referred to as the "Starter Gear". I'm old, and it's a term that I've always heard and used in this part of the country (Southern USA).
It's the part of the starter that's driven by the starter motor and engages the teeth on the starter ring (flywheel).