A few example questions would be:
If you're not too busy, can you wash the dishes when you're done?
I don't think I can; can you wash them?
I've done them too many times this week, don't you think?
The first example has a (preposition?) that can't stand on its own as a complete sentence, and the last example adds a question that would be a fragment on its own, whereas the second example could be rephrased as two separate sentences and read mostly the same. The crux of my question is, if I may make an example of it in itself, are all or any of these sentence structures right or wrong, and should I be rephrasing them as separate sentences? Also, right or wrong, can you provide the terms for those parts of the questions and sentences so that I may better reference them in the future?