Learn Russian: Эти книги одинаковые.

No, because одинаковый means 'identical' or 'exactly alike.' Just like in English, things are usually either identical or they aren't, so it doesn't logically take a comparative form. You will use this word in its standard adjective forms to show things are equally the same.

Does одинаковые mean 'the same' in every situation?

It specifically means 'identical' or 'alike' when comparing two or more things to each other, like these books. If you want to say 'the exact same book I read yesterday,' you would use a different phrase in Russian (та же самая).

Why does одинаковые end in -ые here?

It is an adjective matching the plural noun книги (books). In the nominative case (used when something is the subject of the sentence), regular plural adjectives end in -ые.

Where is the word for 'are' in this sentence?

In Russian, the present tense of the verb 'to be' is almost always skipped. You just place the subject (Эти книги) directly before the adjective describing it (одинаковые).