1) Seller can ask for anything they want, but should probably have some form of written terms. Even on purchase agreement extensions, it should be a formal process. At least from the buyers perspective to add a protective element.
2) Moving on is sort of complicated depending on how your agreement was drawn up. You may lose the EMD - i would consult with your legal counsel.
3) I do think this is a major defect that should not be covered by a simple "sold as is". I would strongly recommend speaking to the listing agent about knocking down the price or asking for recovery. I think you have a high probability of getting your EMD back because it seems like a good argument about the mold being a health hazard.
4) You better not lose your EMD...I will fight them insistently on this. Can't make you buy a home that isn't up to your standards, irrespective of what they say. Especially if they lied about mold before.
Good luck!