Hello Mike,
Here is my take.
1. The best area is the one close to your work. Since you mentioned telco, those are all fairly close to City. As you would want a villa, i would recommend Salwa. However bear in mind that housing is expensive, and a villa will set you back at least 1500 KWD or more. The location of your home is not that important as usually in Kuwait everything is around 20 minutes away, unless there is a road accident. Unfortunately there usually is one.
2. I have a son of the same age, and we managed to find a good nursery. It was not easy, but there are a number of them around. About the schools, they are expensive, and the quality of education is questionable. Our goal is to get out of here by the time our offspring need to start schooling. Also, there is probably a waiting list, so be prepared for that.
3. These are abundant, but I will leave someone else step in, as I haven't used any of them.
4. Daycare we use keeps them very active. There are also public children playgrounds which are nicely equipped. Unfortunately most of the time they are full of trash, so I go there with a trash bag and clean the playground while mini-me runs around.
5. We spend around 200 KWD monthly on groceries for the family of three. And two cats, we found out that our child and the cats consume most of the budget. 
6. Can't advise as I am not from UK, but generally if you are here more than 6 months you don't need to pay taxes back home. Might be different for UK, but I doubt it. Someone will probably chime in.
7. Be prepared to figure out your own way of staying entertained. This is not necessarily bad. Most of the population entertains themselves with shopping, but I am assuming this is not your idea of fun. It also depends on the season, during the summer they need to stay indoors. On the positive side, no one will frown if you go anywhere as a family, like a restaurant or even cinema. There are things to do, but you need to specify what your or your wife interests are. Also, Dubai is less that 2 hours away and is cheap to get to (hint, hint).
8. We considered it and we gave up. It was also foreign to us and it will stay that way. We don't need a maid. We could use a part time babysitter, but such concept does not exist here. 
9. I will not lie; the quality of life is bad. There is a lot to be said, let me know if you have specific concerns. Make sure it is financially worthwhile to you.
I'd be happy to answer any specific questions you may have!
P.S. It is definitely an experience that will open up a while new perspective on life. 