I have some experience with baby bunnies so if you've got any questions just ask.
Covering up the nest is completely natural behavior. She does this to keep the babies warm. To check on the babies just gently remove the top layer and put it back. (If the mother protests while you do this, just take her out while you check on them.)
If the rabbit is friendly enough you can pick up the babies and see if their bellies are nice and round. (Rubbing your hands as mentioned in won't hurt.)
The mother will most likely care for her babies herself. Don't be afraid if you never see her nurse them, she only does this once or twice a day and rarely while you're watching. As long as the babies don't look to skinny they are fine.
You don't have to do much other than make sure she gets enough food, fresh hay and water.
If a baby strays from the nest, just put it back into the nest, as the mother will not lift it herself, and it could risk freezing to death.
The babies will start moving out of the nest on their own when they are 2-3 weeks old, by this time they will also start eating.
They eat whatever their mother eats, but as baby rabbits have even more sensitive tummies than adult ones, don't start giving them greens or vegetables unless the mother was already used to this while nursing them, as it could cause them to get the runs which can be fatal for a little bun
At six weeks most of the babies should be weaned and no longer Dependant on their mother. But they should not be moved from their home cage. Some choose to remove the mother at this stage and let the babies stay together till they are 8 weeks, I just let the mother stay with them.
At 8 weeks they are ready to go into new homes.
If they're not rehomed within 10 weeks they will need to be separated by sex so they don't start breeding with one another or their mother. Males will most likely need their own cage when they are 4 months as this is the time they usually start to fight (unless they are neutered as soon as possible).