Long time since I've made these. I would use flour & milk, plus a tiny bit of salt, can't give quantities as it was just by eye.

Drying slices well on kitchen paper, then a dusting of flour before battering, should both help with adhesion. You are dead right in not using a basket.

If the apple isn't getting cooked through try very slightly cooler oil, so that it cooks slower but longer. Slicing thinner rings will also work, but you are then getting a higher proportion of batter to fruit, which isn't ideal.

Never had the apple running out, so am unsure what to suggest.

A bit of ground cinnamon is good in the dusting sugar, but syrup is supreme. You can see why I don't do these any more, to think I used to be downright skinny.