There are many reasons why a child may get dirty, but there is no excuse for a child to STAY dirty! Regardless of their activities, the daycare workers should make time to AT LEAST wipe hands & face clean of dirt, paint, etc. Sure, accidents happen and clothes gets spills on them, but EVERY day? And for your DC's face to be filthy? No. That's not right, IMO.
I've worked in a daycare center myself. And regardless of what activities we were doing with the children (playing on the playground, painting, blowing bubbles, eating, etc), we washed up after every activity. Period. Even if a parent came by early to pick up their child, if we were in the middle of an activity, I or one of the classroom helpers would wipe her hands & face right then if she needed it. Because we never should send a child home dirty.
But I find your other concerns more unnerving. The teacher had crossed a line in showing affection/attachment to your child. And it seems they changed they way your DC is treated after you complained, that is definitely suspect.
If I were in your shoes... yes, I would take pics. Yes, I would look for another daycare center now. And yes, I would let them know WHY we were leaving, but NOT WHERE we were going. And if there's a way for you to take ALL original files with you, that's ideal, so they have no record of your physical address, phone #s, SS#s, etc.; however, I'm thinking they may need to keep some copy or original for their records.
I wish you the best and hope you resolve this situation soon to give you peace.