My cigarette lighter and my radio stop working suddenly when I pull my 120v converter (that fell to pieces) out of my lighter, what happened?

All of those are controlled by or influenced the BCM. You need a good auto electrician with a pro grade scan tool to check the BCM and communication to and from it.

All of the plastic simply pulls apart, but be careful to pull straight out. The plastic attaching pieces could be brittle. BTW, the whole interior trim disassembles in this manner.
Take your time.

If you have the correct fuses in and they are good check the wires going to these plugs for voltage. If no voltage the wire could be loose or broken. Trace them and see

dig out the 'something' and check your fuses, it probably popped the lighter fuse and one of the pcm fuses

Find a junked breeze at a scrap yard and pull the parts yourself.

Pull one out and see if is blown. The difference between a blown fuse and a good fuse will be abviious.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

The fuse that runs both is blown. Your manual will tell you the location and type needed to fix it. it will probably be a 10 or 15 amp fuse. Most cars have to fuse boxes. One inside and one under the hood. Most likely it will be in the one inside the car. Also, theres usually spare fuses in one of the boxes, so you shouldn't have to buy one. Check and make sure nothing fell into the cigarette lighter socket, like a coin for example. I've seen that countless times. When you find the fuse, pull it out with the white fuse remover located in the fuse box and put the new one in. Hope this helped! Please rate if it did!

Your thought that the end of something fell into the lighter fried something is likely true. I can't imagine that the wire could be fried and the fuse is still good. check to see if the fuse you checked was the right one. If it was and it is good, a wire on the back of the receptacle may have come lose. The end that fell into the receptacle, did it get hot or damaged? That could be a clue as to if the receptacle was shorted when the end fell into it or if not, then look for a lose connection.

So much for chillin out in your car.
What do you mean lighter fell out? Have you ck'd your accessotries fuses?

There are three (3) fuses involved here. The one that is most likely the culprit is the 15A one in the fuse box under the hood, near the battery. Check the underhood fuse box, replace any blown fuses.

The other two fuses (also 15A) are in the interior fuse box, probably left side kick panel.