I would not switch anyone's food anytime soon. The kits will start nibbling mom's food at about three weeks old and will be eating it "full time" not long after. Rabbits are very sensitive to sudden food changes, so it's best to keep mom on the same diet as she nurses and weans them. After that, she could be slowly transitioned back to her normal diet. The kits should stay on the same food until they go to their new homes. It's best to provide the new owners with a week's worth of food to help the babies transition.
Separating the litter depends more on their development and the size of your cage than the age of the kits. If you're working with a commercial breeding operation where does are bred back to back, it's best to separate the kits at 4-5 weeks to avoid overworking the doe. With pet or show rabbits, this simply isn't necessary and can be difficult on young systems. I would wait until at least 6 weeks to make any decisions on separation. At that age, if the kits seem to be doing well eating on their own, separate the 2-3 biggest babies first. Wait another week, then separate the last babies. They babies can all be housed in the same cage, this makes their separation from their mom easier. There are two reasons for doing it the way I described. First, it helps your doe dry up slower. If she abruptly goes from 5 babies to 0 babies, she will still be producing milk for 5 babies. Separating the kits a week a part helps slow down production and avoid discomfort for her. Secondly, it helps the youngest babies with added support before they're weaned entirely.
Gender doesn't matter at that point in time. I'm sure there has been a fertile 6-week-old somewhere in the world, but that's far from common. About 10-12 weeks old is when you'll want to separate by genders (or as soon as you see bucks mounting does, if it happens sooner). I find that my rabbits are fine until this age, sometimes beyond. I usually keep same-sex groups of babies together until I see mounting happening. Obviously it's just dominance at that point, not breeding. But that helps to avoid any little tiffs and usually means they're about ready to transition into the breeding herd.
In closing, I would again stress that you should be handling the babies DAILY from birth. Kits occasionally die for no apparent reason, a doe's milk supply could dry up unexpectedly, a kit could crawl away and get buried where you can't see it. You should be doing a physical once-over and health check daily to make they maintain good body condition, stay in the nest, and aren't injured by a sibling or mom. Handling also helps get them used to your touch, even at a young age. In my experience, those early moments set the tone for the rest of the rabbit's life. The kits that I handle more typically have calmer, more friendly personalities when they grow up. If I am busy with other things or have several litters at a time and can't handle them quite as heavily, the kits are often more "reclusive" as adults. They have good temperaments - not aggressive or mean - and I feel that's a genetic tendency you can breed for. But as far as desensitizing them to handling...it starts in the nestbox.
If your doe doesn't like that, well, she will get used to it.
Rabbits are a little bit like human kids. They don't always know what's best for them. It's our job to know what's best and take action, even if it ruffles their feathers a bit until they realize we mean no harm.