Since no one has answered your question, I'll comment. I don't believe that you have a problem with fungus and in fact I believe that the white spots you see are harmless but I'm not sure. May I suggest that you post your pics on the vegetable forum? I think you would get more responses there.

Good luck.

Here is a link that might be useful: Vegetable forum

You may or may not have a fungus. With damping off, you may not even have fungus that is visibile to the naked eye. If you continue to have problems with these jiffy peat pellets, try something else. I'm not sure if you could sterilize them in some way? Maybe soak them in water to hydrate, then microwave a while?

i used to try to do all the starting inside, i failed all the time. this past year i winter sowed, the best thing ever!! i had so much!! we are going to have so much fruit and veges cuz i honestly thought that i was gonna fail at that also that i just did all of my seeds. LOL you oughta try that!! not to mention it gives ya something to do in the winter!! LOL Medo oh and no dampening off!! and your roots are way awesome!! and when ya transplant there is no shock that i've found!! LOL
you should at least check it out :')) Medo

Here is a link that might be useful: winter sowing

Looks like grey mold