She's only trying to leave the cage because the babies are bugging her. Make sure now that you take her out every day. Mommy needs some alone time.
Wait till 4 weeks to separate. We separated the babies at 4 and a half weeks, and it was fine. You don't want to take them out too early because until they are weaned they need mommy's milk.Male rats reach puberty around 50 days, so you could really go 5 weeks, but I wouldn't wait past then.
How are their colors? Anything interesting?
Baby rats do die often. Though I think your's are all old enough to be expected to live. Also, what sometimes happens, is a mom rat will have a still born and she'll destroy it before you know it was there. Actually I found out that a lot of rat litters have about one still born. Especially if its a big litter.
Just thought you'd like to know.
Lila