"What TV shows do you guys like watching?"
I think it usually would go after the verb. If the verb takes an object, then it goes before the object. If a verb doesn't take an object, then it comes at the end of a sentence.
Is there an example you were thinking of where you saw 什么 come after an object? Like 你们喜欢看电视节目什么？ I don't think I've ever heard anyone say that. Were you thinking of another possible word order?
As a side note, there is a LOT of flexibility in Chinese word order, and adding all the options to all the questions is a monumental task, so just know that the team here apparently favors certain constructions for consistency and familiarity, but there often are many other possible word orderings that are just as valid in Chinese. I can't really think of too many other options for this particular sentence, but I've seen many other examples that have multiple valid Chinese answers, even though the lesson has focused on just teaching one of them.
Well, they are actually two different things. 剧 means a drama, or an opera, so a 电视剧 is usually a TV show with actors and a story, etc. 节目 is literally a "program" or "show" and, like "TV Program" in English, it can be used to describe basically anything on TV.
However, 节目 can also be used to describe the "program" of a live show. So this is often a word that works well for the celebratory variety act type programs that are very common on Chinese television. For example, the big New Years programming event, which involves commedy routines, musical numbers, special tributes, etc.
If we look at the characters, which is a dangerous game to play, but here might yield some insights, 节目 is "festival-eye" so it has more of the connotations of the word "show" than "program" which in English alludes to the scheduling.
So ultimately, you could take a Sitcom and call it a 情景喜剧, a 电视剧, or a 电视节目. But you couldn't go the other way, since not all shows are dramas, and not all dramas are comedies. As a general rule for translation, it is important to never use a category more specific than the one in the original language. (You'll see this mistake on duolingo most frequently with the hoards of Americans on Duolingo in every language who are demanding the right to use the word "England" or "Britain" to translate the terms various languages have for the United Kingdom.)