Learn Polish: Gdy mam czas, czytam książki. - When I have time, I read books.

In Polish, the verb endings already tell us who is doing the action. Both mam (I have) and czytam (I read) end in -m, which is the typical ending for the "I" form. Adding ja isn't necessary unless you want to emphasize it.

What is the difference between gdy and kiedy?

In this sentence, there is no difference! Both mean "when" and you could easily say Kiedy mam czas, czytam książki. However, kiedy is also used as a question word (like "When do you read?"), while gdy is only used to connect statements like this one.

Why doesn't the word czas change its ending here? Isn't it the object of the verb?

Yes, it is the direct object of "I have", so it takes the Accusative case. However, czas is a masculine inanimate noun (a non-living thing). In Polish, masculine inanimate nouns look exactly the same in the Accusative case as they do in their basic dictionary form.

How do we know książki means "books" (plural) and not just "a book"?

The singular word for a book is książka. The -i ending on książki makes it plural. Just like time, it is the direct object of the verb, so it is in the Accusative case. For most plural nouns, the Accusative form is identical to the regular plural form.