Learn Dutch: Ik wil op zondag uitslapen. - I want to sleep in on Sunday.

You could, but it changes the meaning. 's zondags specifically means "on Sundays" as a recurring routine (every Sunday). Using op zondag simply means "on Sunday," which in this sentence likely refers just to this upcoming Sunday.

Why does uitslapen go at the very end of the sentence?

This happens because of the modal verb wil (want to). In Dutch, when you use a modal verb, the second verb (the action you want to do) gets pushed to the very end of the sentence in its full dictionary form.

I thought uitslapen was a separable verb. Why isn't it split up into slaap... uit here?

You only split a separable verb when it acts as the main, conjugated verb in the sentence (for example: Ik slaap op zondag uit). Because wil is the conjugated verb here, uitslapen stays at the end in its full, unseparated infinitive form.

Is op the standard preposition to use with days of the week?

Yes! Just like in English where we say "on Sunday", in Dutch you use the preposition op with days of the week, giving you op zondag.