1. It's forbidden to swim in the lake - You can't/mustn't swim in the lake.

2.Is it OK to use your insect repellent? - Can or Could I use your insect repellent?

3.It's possible to see alligators there - You can see alligators there.

4.We are allowed to put up our tent here - We can put up our tent here.

5.Alligators aren't able to move fast in circles - Alligators can't move fast in circles.

6.It's possible that you will get lost there - You can get lost there.