If I touched some of this "dried" sulfuric acid could it have burned me since hands are moist?
No.
Would it have been obvious?
Yes.
Would the spots I walked on have transferred to my shoes and could that have burned me when I took my shoes off?
No.
If it did start burning my hands would it transfer to things I touched throughout the day?
No.
Or, more precisely, if it would start burning first thing to do is to wash your hands with copious amounts of flowing water. After that any acid present would be rinsed and there will be none left.
So is it getting diluted from the water in the air?
A bit. It also dries up, so even if accidentally spilled and not cleaned up it won't stay there forever. As long as these are stains and not poodles there is nothing to worry about.
Even if I got some trace amounts on my skin would the other day would it not be a huge issue?
No.
The scariest thing for me having a chemical phobia is the idea of it contaminating everything I touch and getting burns over and over when
It doesn't work this way, don't worry.