I don't know what the spots are, but I think this plant is quite healthy; as for the smell, most soils have some smell. I don't think those filaments are anything dangerous, maybe root hairs? I should be glad to hear the opinion of wiser folk here. A grittier compost might be an idea, you seem to have a lot of peat there.

He had more white mold before, but I took it down before I thought about taking pictures. It was much more developed first time I found it. And I stopped water it after that, about 5 day ago. I used to water it once a week but I didn't know that doesn't like to have water on the bottom of the pot.

Here's what I would do: Get a slightly larger pot (clay or plastic) with holes in the bottom. Repot using a faster draining potting mix which would be commercial cactus and succulent mix which you would combine 50/50 with perlite or pumice which is available in nurseries. Rinse the perlite or pumice through a strainer before mixing with the commercial C/S mix. Get all the existing potting mix off the roots. Use a fork, your fingers, whatever to get as much off as you can. After repotting, do not water for several days. Also, I don't like to see succulents double potted as yours has been. They do better with full air circulation around the pot. You have a nice plant there, but it needs a repot. Looks like you have taken good care of it so far. When you do water it, let the water run out the drain holes, then don't water again until it's quite dry.