Dogs and young children are really, really difficult to manage. I have 21 years of dog ownership under my belt, plus professional canine behaviour qualifications, and I find it difficult to mediate between my 3YO and the dogs at times. might be better if I had any clue about small children
A) Depends on the dog. Probably don't get a greyhound. If you got a pup the cats would probably gang up, as sam says. You might get a rescue that's good with cats.
B)That's because most dogs will be happier with older children, I'm afraid. We looked long and hard for our boy as we have a 3YO DS. (Girl dog arrived before DS)
C) Maybe. Maybe not! Depends on the dog, and if you know what you're doing. My first dog picked it up very quickly. Second dog was a rescue but not toilet trained - first dog taught her quickly. Third dog came toilet trained... and so on.
D) Dogs usually come with us. Occasionally we have to go where they can't come (eg visiting in laws) and my mum will have them. Couldn't do kennels as mine are rescues and would probably be quite traumatised!
E) Completely down to preference, personally I find puppies bloody hard work. Our boy came to us at 9 months and that was younger than I'd normally go for, but he's fab in most other ways so I let him off! Aside from being hard work puppies are very impressionable, early experiences have long term effects. You need to get a good trainer from day 1.
Why do you want "smallish"? What are your requirements from a dog? IME smaller dogs are often much harder work than the bigger lazier dogs.