Scary moments - what temperature for broiling?
Assuming you cannot fix the oven (which would be my first recommendation as much for safety as anything else), then for browning things on the top I'd suggest using a cook's torch, which is the same thing as a plumbing torch except it's flashier. 

Of course you'll want to make burgers, steaks, fish, etc as well. Baking these will not get you nice toasted brown bits no matter how hot you set your oven, so frying is your next best option although in some cases you could use the torch there as well. 

You could your too-hot broiler question on the diy forum to get ideas on fixing it.