None of mine have hides unless they are a hatchling or juvenile. Once they hit 500+ grams I yank the hides. The hides are really only for the young ones because they tend to be finicky eaters. If you really want you can leave the hide in, I don't see how it would make a difference, but if you can take it out, I would consider it. You can put black construction paper on the tub to block out the light on three sides.
I always move the male to the female's tub. That way it causes the least amount of stress to her. The males can get over it, they are too busy thinking about other things. And no, don't put them in a new enclosure. The smells of the female help entice the male, especially a fresh shed-still in the enclosure.