Can I Produce Portraits Of Characters From Films And Sell Them In Shops?

To be able to sell your drawings in shops, you would have to obtain the permission of the film company. For example, if you wanted to draw portraits of characters from The Lord of the Rings films, then you would have to write to New Line Cinema to gain permission, and the same goes for the Harry Potter films, which are owned by Warner Brothers.

People who charge people for fanart commissions technically shouldn't do this, as they are making money from something that doesn't belong to them.

Some film companies already have their own artists who produce art for film merchandise such as calendars, books, games, t-shirts etc.

Fanart is allowed, but not for making money. The best thing to do would be to produce your character portraits and share them with other people by posting them on a website. If people like your portraits, then perhaps they can commission you for something that is not related to the films.