Ok, here's some words, not sure how wise they'll be
Had he mated with all the girls? What is he like left with them? I'm wondering if you could just let them all live together or if he really does have to be taken out? Some billys are aggressive, others not. But obviously if you have females you don't want mates that's not a good plan. Could you have a 'grown ups' and 'female youngsters' field instead of a male and female field? That depends if he's nice to the girls or not.
No, not a good idea to keep a horned and unhorned goat together.
Obviously it's not ideal that he's on his own but if he has to be, better that he should be near the house and with plenty of coming and going. Phew, you have a better stomach than me, keeping a billy near the house
Do you have male sheep he could hang around with instead. This is best away from the smell of inseason females, of either species, since that might cause them to be bolshy with each other, whereas generally they can get along fine if there is nothing to stir them up.