Yes on rainbow trout.
see this. It isn't that daunting, but setting up the pump can be the hard part. Once that is good, it's easy and just takes time letting it run. And if it rains a lot, it may take longer. I would price out the pump, and the amount of lime you'd need to see if its in your budget.
Hard to say how long it would be to fill again. Mostly weather related, and that's to big of an uncertainty. What source normally fills the pond? It would be faster if it had a constant water flowing in, like a spring. But if that's the case, its harder to pump out.