1 (a) If you train females, then this would violate the principles of modesty, as it entails showing them physical workouts and body positions. So generally it would be haram.
(b) If you will be training males only, and the environment directly around you is appropriate then it’s fine. But if it means you will be regularly around females in their gym clothes, and you will not be able to avoid seeing them, coming across them, or interacting with them, then it would be haram.
2) Yes in that case, it would be ok Insha’Allah