I don't think she can have your little one as i think you can only have one child under 18 months and hers will be that one. the child ratios are quite strict. have a look at the national childminding association website. they'll have the regulations for you.
The vast majority of childminders if working alone are only registered to have 1 child under the age of one and if they have a child under one themselves they can not usually have anymore.
The exception usually being if they take on twins. You must look at her registration certificate to check the numbers and ages of children she is allowed to mind.
Can't help with anything many of your points, but my childminder will be looking after my dd (10 months when she starts) and another little girl (6 months). She has to get registered for this and is going through the process at the moment. Childminder has said that she will be buying a double buggy to transport the children.
As everyone has already said, she can't have two children under one as her own child counts in her registered numbers. Personally, and obviously this is just my opinion, I would never use a childminder with a young baby of her own. Of course she will give preference to her own baby if she is on her own and both of them are crying/need something at the same time. The best childminders I have used had school age children of their own so lots of experience with children, but no obvious favourite. I went to visit a local childminder when looking for childcare for my 18 month old last year - there was a mother and two daughters working together in a dedicated space which sounded great, but when I got there one of the daughters was cuddling her own baby and the toddler she was responsible for was crying on the floor. I overheard her sister refuse to comfort the the child as she wasn't "her" child - no way!
maybe 4 mth old is a bit young for her to start work looking after other babies, personally i wouldnt feel like it although i did care for another child of 10 mths along with my own of the same age, but let her have a try if you feel confident in her , thats the importanrt issue here, do you feel o.k about going back to work leaving your child for the first time with her, everyone has their own values as to what to expect and i certainly wouldnt lower my standards if i felt it wasnt right , maybe i am more choosy and look into things too much as i`m a N.N..E.B AND CHILDMINDER WITH 20 YRS EXP SO know what to expect, but maybe you could give her a trial or even spend one day with her to see how she manages, its a perfectly acceptable condition to ask for and i wouldnt mind , in fact i could probably get to know the parents a little better this way. also do a few hours here and there and arrive earlier to see how she`s coping.good luck and go with your gut instinct
My childminder got an exception when her daughter was a baby. However, I'd be reluctant to use a childminder with no experience, whether or not she had her own baby. I'm quite sure mine was fabulous, but then she'd already been working in childcare for years.