#1 is an Alocasia, not 100% on the variety though. Perhaps sanderiana? #2 looks like Peperomia magnoliaefolia variegata. I've never grown either so I don't know much about them. All I've heard is that Alocasias can be finicky. Good luck and happy growing!

Almost positive it's leaf blight now, especially after looking at pictures and reading up a bit more. It's spread to two of the other leaves. I should have some fungal spray at home that I'll try out this weekend. I'm also planning on repotting it since I heard that fungal blights (oomycetes?) can get down into the soil and remain dormant there. I haven't noticed any sort of blight on my other plants (Potentially some on a zebra plant I got, but I'm more inclined to think that's stress from low humidity or poor watering conditions from the previous owner), so it doesn't seem to be spreading, and I'm also almost positive that the plant came with it. Soil's drying and I've ceased misting it because water apparently can spread spores. anyway, if worst comes to worst, can I just take the leaves off and try to get the tuber to send out new shoots? I've heard of alocasias going dormant for a few seasons and can be kept relatively dry and won't rot.

Alocasia x amazonica, perhaps. Here is a link that might be useful: Alocasia

I grow amazonica-type hybrids in pots as houseplants as well as in the yard and greenhouse. The ones I grow in the house are huge old plants, multi-trunked specimen plants. I have a loweii that is almost 10 years old. The others are Polly and Purple Prince. I water these all ONCE A WEEK. That's all. I totally saturate the soil ONCE A WEEK. They grow under a bank of skylights in what amounts to full sun for about 8 hours daily. Brown edges on yours could be either too much moisture at the root level, or humidity too low.