Looks like it'll clean up great! Did it come with glass and a lockdown bar? It's a pretty basic layout but those four flippers in that configuration look to be fantastic for practicing on. Reminds me a bit of Sharpshooter.

As for your questions:

If it goes straight to ball three I'd guess there is an issue with the reel that tracks balls. It might be damaged, slipping, or in the wrong location. Does it do the same thing for both players? Is the machine set to three or five balls?

Free Play- probably not, some EMs can be jumpered to act like they are on free play and coin up when you hit the start button but I don't know of any that have a setting for that. If the coin mechs are working you can probably just open the door and flick the switch a couple times. Some people install an extra button that does the same thing as the coin switch. You could also just use a cup of quarters, that has something to be said for it.

Plastics and playfield are going to be really tough. Most of the time with EMs you're going to be better off getting the playfield touched up than finding a replacement. Plastics would probably be a one-off from scans of someone else's that are in good condition. You could post a want ad on the marketplace though.

Cleaning- I don't know there, haven't done it myself but there are some other threads on it. The paint isn't flaking or rubbing off, is it? I wouldn't use anything abrasive like Novus or magic eraser to start with. Try a damp microfiber cloth before anything else.

Depopulating- With that layout, you really shouldn't have to if all you're going to do is clean it. You're going to spend hours just getting the pop bumpers in and out the first time. Remove the plastics and you should be able to get most places that need to be gotten to. Also, if it's all working now just keep in mind that it might not all work when you tear it down and then reconnect everything.

Also, welcome to the club! I feel like there are more and more people in their mid-20s picking up machines, maybe it's just me. I guess that makes two of us, at least. Three if I count the other guy I know around here.

Nice! When you said broken plastics I figured you meant the art. For that lower guide plastic you could probably just trace it out on something you pick up at a hardware store and cut it by hand. That or just get some plastic glue and weld it together. It's not something you'll see at all while playing. Those pop bumper caps look really nice and I bet those would be the hardest thing to replace.

Definitely get some new rubbers and balls! Old balls with scratches or corrosion will chew up your playfield quick.

Try grabbing the playfield under the apron near the drain and lifting - you should be able to get it out although not all playfields have rails or a pivot point. You shouldn't have to disconnect anything as far as I know. I haven't worked on any EMs myself though.