Chosen Solution

I got the charger from eBay recently (yeah, it isn’t a good idea in hindsight) and I have the issues described in the title. Is there a way to tell if my MagSafe charger is fake?

What the system working before you used this charger, and did you smell the burning when you plugged in the charger? As far as telling if you got a knockoff it would be really impossible without breaking the case open and in doing so you would remove the possibility to have the seller responsible to have your system fixed and getting a new charger. You may have major damage within your system from the over voltage. I think you’ll need to find your way to an Apple Store to get an estimate on the damage. Most Apple Stores don’t charge an estimate fee while a reseller will as well as an independent shop.