I have eyes selected and they don't appear on my avatar... Also, I have a recurring problem where suddenly I can only select from 4-6ish rows of items in my wardrobe.
can you double check that the eyes layer is above your base? i was able to add eyes to my ha and save with no problem, so i'd say check that first. if you're having problems with eyes that are an item, make sure you own the item first. if you don't own the item you can't wear them!
the second problem i think is due to the avatar image itself in the wardrobe overlapping with the items. if the avatar image is over them you can't select them. try zooming out in your window. unfortunately i believe this is a known problem.