I got a question about powering the car...

Several ways, depending on your interests. You could connect to a local GI bulb. I prefer hard wiring (soldering); but you could cheat and use alligator clippers to make the connection (many pinball mods use these, I don't like them since they eventually vibrate off. If you have bad luck, they can vibrate around and cause a short).
This would keep the lights on throughout the game.

I have mine wired to the the Jackpot insert light. This light is on a green light board, and makes connection a bit more difficult.
A few ways to do this....
1) Use automotive quick splice connectors and connect to the wires connecting to the green board (you will need to trace which wires are lighting that insert). By far the simplest, and easily reversible.
2) Could drill holes in the plastic 555 bulk connector (black plastic). Connect the wires inside the bulb holder....
3) Solder the wires to the solder pad where the 555 bulb holder makes contact. It's not pretty but will work.

Hope this helps....

I'm already thinking about the next one. The bear rug...

Again, i have nothing to compare or copy (except what i see online).

But it looks like the bear is actually from a plastic toy. Playmobil bear rug (brown). It looks like it went to a castle set.
Ebay seems to have them. Paint the bear white. In a few weeks, will look to build one with LED's

Awesome.. Thanks. When i get some free time, the bear rug is next.