Of course. They should be out and about on sorties for a week now. Curious little critters.
They also need access to mums food (and, well, poop too), so they can start eating solids.
Either replace that bowl with something shallow where you put the nest in (or just remove the plastic thing completly, a corner is fine for the nest now, I would add a pile of hay), or make ramps outside so they can always get back in.
No. The doe will do just fine, her motivation is to get rid of the milk, she'll find the kits. Actually, you might want to put a shelf, some elevated place in there that the kits can't reach(now), they can pester the doe once mobile, so a place to get away from the little brats would be highly appiciated.