"I do not want him to have a television."
Translation:Ich will nicht, dass er einen Fernseher hat.
Yes, marziotta is right, it changes the meaning a bit. "Ich will, dass er keinen Fernseher hat" means that you are absolutely against it, that he has/get a TV. "Ich will nicht, dass er keinen Fernseher hat" means that you're more concerned that a TV is not so good for him. But the difference is negligible. In the end it all depends on in which "tone of voice" to pronounce a sentence. This is the same as in English.
Generally always yes in the spoken sentence, in written rather no. German is a lyrical language, you can see it in "how we speak english" :-D, that makes it complicated. But do not give too much thought, we are talking simple colloquial German, and in our "everyday" language we are also do not talking lyrically, unless we want to bring something to the boil. If you come as a tourist, and you find no words, English can help :-)
"Das Fernsehen" is television, the TV programs and everything together, television as a whole medium, while "der Fernseher" is the TV set, the thing that you watch TV shows on. In this sentence, we are talking about a device that you can watch stuff on, which is "der Fernseher".