How does one make a mistake like this is beyond me. Yes, it is a problem. Get someone to take you to an auto parts store to get a flush and fill kit. NOW. DO NOT DRIVE THE CAR, DO NOT START THE CAR. GO NOW!!!
It most likely will not hurt anything as it is such a small amount. You could drive it like it is or drain it and refill with the proper mix of antifreeze and water.
You put a plumbing rain cleaner into the cooling system "by mistake"?!! LMAO!! What happened? Did you get a turd stuck in the radiator when you thought it was the toilet?!!
Definitely not good as it will corrode many of the alloy parts and gaskets in the engine. Have it flushed thoroughly asap.
Yes. All the aluminum parts have been eaten up a bit and dissolved.
You will probably have the cleanest cooling system within 100 miles.
