1. My favorite is music (which was/which is) written by Mozart.

2. I am reading a book (which was /which is) written by Hemingway.

(which one is right in the parentheses?)

3. After use, just take them off and wash the fat away.

(What is the meaing of "just' in the sentence?

1 and 2 -- "which was"

In 3, "just" means "simply."
http://dictionary.reference.com/browse/just
See #s 11 and 12 here.

1. The correct choice in the parentheses for the first sentence would be "which was." This is because Mozart is a composer from the past, so his music was written in the past.

2. The correct choice in the parentheses for the second sentence would be "which was." This is because Hemingway is an author from the past, so his book was written in the past.

3. The word "just" in the sentence means to do something immediately or without delay. In this context, it suggests that you should take off whatever is being referred to and wash away the fat promptly or right away after using it.