If you change 'продавал', 'продавала', 'продавать', 'будет продавать' to 'продал', 'продала', 'продать' and 'продаст', they will be correct. They are better with perfective aspect because you are interested in the action as a whole, as a single point, not in the process of development.

1. all the senteces containing both 'he' ans 'his' would be uniformly understood as is 'he' and 'his' refers to two dfifferent people. Even in this case we would prefer to dismbiguate it with naming one of the two persons. If 'he' and 'his' refer to the the same guy - then it is он.... свою... 2. Grammar is correct everywhere. But you are using imperfective. A simple way to understand (at most part:)) Russian perfective is by exclusion... imperfective is used for - continuous action - repeated action/usual state etc. As one hat could hardly be sold usually or repeatedly... it will be understood rather as "whether he was selling his hat", "whether he has been seeling his hat" etc. The perfective form would be more like 'get sold' then 'have sold' And now, I don't understand English well enogh to fugure out, what do you mean here:) By 'wants to sell' you probably mean "wants the outcome: some money, no hat". Well, sometimes we use imperfective in such situations to add just a slight shade of doubt (when we really don't think about the_process_, but name the process). Perfective is the norm. With 'whether he sold'... I thought you would use 'have' if you mean the outcome, not the process?

I am not a teacher, but on my mind your sentences are absolutelly correct in one way. However we can write it down using perfective verbs. In your version, you wanted to say that something were being sold. However, if you wanted to say that something was sold, you should have written it slightly diffirent: Я не знаю, (продал) ли он его шапку. (second version) perfective verb I don't know whether he sold his hat. Я не знаю, (продала) ли она его шапку. ( second version) perfective verb I don't know whether she sold his hat. Я не знаю, хочет ли он продавать его шапку. (needless to correct) I don't know whether he wants to sell his hat. Я не знаю, хочет ли она продавать его шапку. (needless to correct) I don't know whether she wants to sell his hat. Я не знаю, кто (продал) его шапку. (second version) perfective verb I don't know who sold his hat. Я не знаю, когда она будет продавать его шапку. (nedless to correct) I don't know when she will sell his hat. Я не знаю, где он продавал его шапку. (second version) perfective verb I don't know where he sold his hat. Wow! I am astonished ! You made a big progress !!!

Almost.