It sounds like taming and familiarisation is going well. You can make a house from a cardboard shoebox
. Just cut the base out, keep the lid for a lift off roof and cut a hole for a door. If it’s too big then a tissue box. Yes the bugs must be driving you crazy. They won’t do your hamster any harm - he might even see them as a tasty snack. Grooming is normal - they groom a lot.
I can only think it’s the food or something got missed during the cage clean and eggs hatched out. Yes try changing the house. Squish any bugs you see and maybe that will be the last of them.