Can Energy Transfer be cast repeatedly at the new Livid Farm, or is there a time limit between casts or something to that effect? (In short, do I ever have to train Agility the normal way again?!)

No.

 

You can only cast Energy Transfer when Pauline is drained.

Above poster is correct.

 

Also, it seems like you can only cast it on her once ever 2 cycles in my experience. It's like barbarian fishing for sturgeons...I suppose it can train agility but you'll do it at such a slower rate than usual, I wouldn't recommend it as your primary agility training.

In my experience Pauline draining is not even 100% every 2 rounds. Sometimes she goes for 3 rounds without draining and sometimes she drains twice in a row. But 2 rounds is definitely the average.