Say if a Porygon-Troll traced a Trollems sturdy. Trollem used earthquake, and then switched out and switched back in giving Porygon-Troll 2 turns to recover from having 1 hp left. Will sturdy work again?
If you mean.... if you have a Pokemon with sturdy, and you recover it to 100%, will sturdy work? Well, then, yes. Though I don't think any Pokemon that can have Sturdy can learn any recovering moves. No wonder you did the trollem thing...
Yes, as long as you have full HP with Sturdy you can not be OHKO'd unless by a multiple hit move, and there is no limit to how many times Sturdy can be used as long as you have full HP each time.
Yes, Sturdy will work everytime time you have full HP.