A mosque is a Muslim "church" there are no Christian churches in Doha yet, but a couple are in the process of being built and the hotels have some services.

You can get internet in your home and satillite TV, all the comforts.

Immunizations, if you go to the doctor they might give you a Hepatitis shot, but thats a general percaution for Asia, and I don't think it is a vital neccessity, Qatar is very Western. You will probably be more surprised by the similairties between Qatar and the US than the differences. The only thing you might notice (disease wise) with your kids, because this happened to me in Korea, is that they will get every cold and flu bug they come across when they first arrive, this is because they are slightly different than the ones in England or the US, but thats a general thing for anywhere you go.