They seem to like a lot, and extra plants probably aren't going to hurt anything. Plus, if you're interested in keeping all of the eggs, you'll want to remove them before they get eaten by the adults. The easiest way to do that would be to swap out elodea strands (it doesn't need to be rooted to stay alive). Or you could also cut off the leaves that have eggs glued to them.
My females laid from November to January usually (but they started early this year) so it might be easier to remove eggs rather than the female. They also seem to lay more often in the morning. I take the male out every few days to give the females a chance to relax. He has a bachelor pad
You can probably just keep any eye on them and look for signs of distress in the female before removing him.
As for feeding the larvae: I've used the pond water method (described in the CC articles section), and purchased Moina for them. I'm brine-shrip impaired, so I haven't used them, but I hear freshly hatched brine shrimp work well. The newt larvae are really, really small.