Cheese in the traditional way, probably not. I think it relies on a chemical reaction that's fairly unique to lactose (and lactose is, as far as I now, a sugar unique to milk). At least I haven't seen or heard of anyone doing it (except a few biotech firms that are explicitly working on novel ways of achieving similar chemical reactions). If such a product exists it's really badly marketed (or very low volume), because I know many vegans that would pay a high premium for such a product.

Yogurt is basically milk with a bacteria that eats sugar added to it. You can do that with any product similar to milk it seems. Oatly produces an oat-based yogurt, and the Swedish market has yogurts based on (at least) soy and lupine as well.