"My older brother watches anime on TV every day."
Actually I think he's right....i'd get my grammar dictionary out but I'm Waaaayyy to lazy to do so....
Questionable link + remembering being taught that te iru does include habitual action... TE IRU would be used here! This sentence is incorect!
I think you're putting too much of your own interpretation into it by using that grammar pattern. The Japanese sentence you have emphasizes the fact that anime is all he watches, or all he does is watch anime, whereas the original Englih sentence "My brother watches anime on TV everyday" is much more neutral.
I don't have any proof either, but I agree with you; I've heard the "every x" part at the start of many sentences too.
My guess is that it's just not the most natural option, and the course creators just haven't added it as an acceptable answer for this exercise. You should report it for them to fix.
It's a difficult one, because it is correct both ways. It's like saying, "My brother is watching TV every day", and switching out for, "My brother watches TV every day". In the same way as English, there are multiple ways of saying the same thing in Japanese! Hope I've been of use! :)
It would make an ungrammatical sentence. に implies some direction to the action, like "to the TV", which doesn't really make sense with a verb like "watching".
Note that the role of で in this sentence isn't related to location, but rather it is denoting "by means of", i.e. "My older brother watches anime by means of the TV every day".