Key stuck, won't turn, won't shift...replace ignition switch?

Try to shift your key in either direction while try to turn your steering in left and right direction. May be its steering lock which is attached to your ignition key preventing shifting of key. If not, then its obviously your ignition that has gone.
If you decide to change ignition then as a last try Dip your key in lubricating oil and then insert in ignition to turn it on. May be it can help.

No! The car shouldnt be used to charge the battery even though it may be able to tdo it its not the design to the charging system and you can melt stuff as the altenater charges the battery too fast and ( hot ) to be a good thing. If you can remove the key and it won't run in either dirction and the steering wheel isn't in a load so the key is held against the lock. Yes you could have melted the electrical part of the ingition switch. Now the battery isn't out of the woods either and after this hot charging try the altenater could have been damaged so the battery is on the way to the parts store to be tested and or replaced and the altenator might want to go too. Sure if they pass put em right back in.

Before you replace the switch try this. As you try to turn the key rock the steering wheel back and forth. The key may turn then, if so it was stuck due to pressure from the steering wheel lock. If it still doesn't turn yes the key and tumbler are bad.