I personally would also be sceptical about letting the worms/crix loose in the cage; both will burrow down into the mulch, and while tegus will often detect them and dig them up, you want to avoid having feeders loose in there if possible. Keep the worms in the dish, and maybe tilt it slightly so that he can see theyre there.
I would start looking at making pinkies a part of his diet; if theyre half the size of his head then he should be able to take them, and they are nutritionally far more sound than a lot of foods. Crickets and superworms will still make good staples at this stage however - most people tend to give up on the crickets only when their animal gets too large to catch them effectively
Gradually increase the size of the mice as he gets big enough to take them; chicks also make a popular choice of food.
Keep an eye on the sneezing. Is your substrate dusty? A daily misting to keep things slightly moist should help cut down some of the dust, and will hopefully resuce the sneezing. If it worsens or your animal shows any signs of trouble breathing or wheezing/discharge from nose or mouth get it to a vet; respiratory illness is serious, particularly if its got to stage when your animal is quite visibly sick.
With regards to skittishness - if youre coming at him from above then it may frighten him as he cant see accurately whats coming down to him; he may think its a predator trying to surprise him. Try to touch him from the sides rather than the top.
Good luck
Im sure it will be fine.