Draw the structures out.
First off, why are there (according to a problem in my book) only two ethylheptanes, 3-ethylheptane and 4-ethylheptane? Why can't 2-ethylheptane exist?
The parent name is the longest carbon chain. When you add the ethyl-group, the carbon back-bone can change. As a result, when you put the ethyl group on the second carbon in heptane, the longest carbon chain becomes 8 carbons long, and thus no-longer heptane.
Also, would 5-ethyl-2-methylhexane be an isomer for nonane?
Again, draw the structure. What is the longest carbon chain? That is not a valid name. Once you draw the structure and name it properly, you will see it is on your list.
Likewise, would something like 2,3-diethylpentane exist? If it doesn't why not? I think I'm missing something crucial here and I can't find it in my book.
Again, draw that structure. The longest carbon back-bone changes, the name changes. It again is on your list.