Do you let campers swim in the lake during the spring/summer?

Yes. Unless there is a flood. Last year we had crazy rains and the lake was flooded, the swimming area was closed. You should be fine now.

There are swimming areas

Yep two swimming areas, one in loop 2 and one with public access past loop 3.

Yes, there are at least two designated swimming areas (there could be others we didn't use).