Though a dog owner, I'm not a rat terrier owner but can offer some suggestions. I did a quick search in google and found a lot of information out there about rat terriers.
1. Does a Rat Terrier get along well with kids (when it grows up)?
Most agree that they are great family pets though some argue they are not the best for small children. I suspect this is due to their high energy and individual owner's training of the dogs. If you are committed to training then you should have no problems with them around smaller children.
2. Does a puppy (as in, a few weeks to a few months) need lots of running around?
Puppies in general are full of energy but I suspect a rat terrier will be even more energetic.
3. How old do they have to be to be separated by their mother?
Puppies are kept with the mothers until 6 to 7 weeks.
4. Grooming
http://www.terrificpets.com/articles/102100065.asp5. Feeding
About 1/4 to 1/2 cup of dry dog food a day.
6. Anything else about raising a puppy?
Puppies are like raising babies but way more intense. You go through all the stages of babyhood such as potty training but a much faster pace. Also be prepared for some damage from chewing and accidents.
7. The cost to buy?
Cost will depend on the area you live in. The best thing to do is look at the classifies and breeders in your area. Some people go as far as shipping one from a breeder but this could become costly and isn't advisable for the stress it puts on the animal.
