Now as far as the other info. First make sure she is pregnant and indeed a female. Do you know how to sex rats? I am asking because you were not sure of the sex when you picked them up. Anyone obtaining rats from a petshop and keeping them together should know how to sex rats before doing so. If you need help I can snap some photos right now if you'd like.
Because if indeed she is not female, and a male, seperating her from her clan is going to do more harm than good.
PLEASE take the male away from the females. You mentioned you had him in with the older doe as well. You do not need more babies if ones are on the way. Any breeding should be done by someone with a good knowledge of genetics, homes lined up before hand etc. So if you can please remove the male from the cage. You mentioned the others were fighting. Give them time, introduce them on neutral ground and they should eventually come around. Rats are very social animals and do need to be kept in same sex pairs or more. It's very un-natural to keep rats seperated.
Rats can get pregnant the moment after giving birth. In fact, even does who are not in heat can be stimulated into heat by the males actions and become pregnant. Rats go into heat every four days during the night. Do not mistake fighting for playing/dominating. If there is no blood drawn everything is fine. Rats squeek constantly when being force groomed and when they are trying to work out their status in the colony. I would try to introduce them slowly again on neutral territory. Scrub and disenfect the cage and add all new bedding and then they will work out their own heirarchy on their own.
One thing I am concerned about is that you did not quarantine these new rats, and since you have other rats already at home who have been exposed I would be worried about viruses such as Sendai, SDA, and even bacterial diseases such as CARB being spread throughout your colony. Every rat that enters a new home especially from a petshop should be quarantined for a minimum of at least two weeks in a seperate home or a seperate air space. Viruses such as Sendai and SDA spread through the air and are highly contagious. They can wipe out a whole entire colony of rats in days. It's a very serious threat. I would watch for any signs of illness such as sneezing, raspy breathing, staining on the eyes and nose etc.
Now if she is indeed pregnant keep her seperated in a 10 or 20 gallon tank. Make sure she has plenty of fresh food and water at all times. You will need to up her protein and fat content. Offer safe fruits and veggies as well. If you want to learn more about what to feed your doe during the time she is pregnant as well as what to feed the others (just in case you were curious) I would suggest reading my feeding article here:
Also make sure that when the babies get there you keep mother and babies quiet for a few days. While most experienced breeders do handle their babies the first day or right after birth I usually do not recommend the layperson do this. It can stress the mother out. However if she has no problems with you even getting near her and touching the babies then you can handle them. I would suggest at around three days trying to take the mother out to let her get some exercise and then handle the babies very gently. The first day they will need to be checked for a milk band. You can just peer into the cage and this is very obvious. They will have a light band of milk in the stomach. They are pretty see-through when they are born. If you do not see a milk band in the first several hours then I would be worried the mother is either neglecting her young or not producing milk. I know I am saying so much at once LOL, but all this really needs to be said. So around the third day if you do not need to intervene any with raising the babies, the mother should be a little less stressed and handling of the babies can occur. Rats babies need to be handled very frequently so they grow up nice and tame. It also stimulates their brain and makes for a more well socialized pet which is going to help when it comes time to place these babies in new homes. I usually take my babies our for about 10 minutes each day in the first week, and gradually build up to more and more time out each day. Just be very careful when you handle them, as dropping them could lead to their death. If you are uncomfortable handling them so young wait until their eyes are open when dropping them isn't going to do much damage, but they will also be fairly more active. Once their eyes are open at around 14 days they start pop-corning and become quite hyper.
If you want to learn more about what the actual birth entails and find out more info on how the babies grow you can visit my reproduction article here:
I hope this helps and if you have any more questions just ask! Good luck! Rat babies are sure cute. You should have a load of fun raising them.