These are my thoughts:

1. Is is usually in their house or is it possible they drop the child at my house?
Almost certainly in their house. Parents want their kids to feel comfortable and the easiest way to ensure that is having them in a familar environment. Also, it'd be scary to have someone you don't know very well take your child to their house.

2. Is it usually paid into a bank account or is it mainly cash in hand?
Cash in hand.

3. Do you think the clients would tend to mind if i have my 4 year old with me while looking after theirs?
They probably would :/ It's a bit unfair, but I do think parents probably want you to be focusing on your child.

4. Would having my own child be an advantage as it shows I know what im doing?
It is good that you're a mum. You can do a billion courses at uni but the best experience is having your own.

5. Is housework usually added into the service?
You can probably charge a little extra per hour if you do housework, but I do it for free.