Learn Italian: Voglio esprimere quello che penso sull'universo. - I want to express what I think about the universe.

In English, we use "what" for both questions ("What is that?") and statements ("I know what you mean"). In Italian, when "what" means "the thing that" or "that which" in a statement, you must use quello che (or ciò che). Cosa is primarily used for asking questions.

Could I use ciò che instead of quello che in this sentence?

Yes, you can! Voglio esprimere ciò che penso means the exact same thing. Quello che is very common in everyday spoken Italian, while ciò che sounds slightly more formal or written, but they are completely interchangeable here.

Why use sull' instead of dell' or all' to say "about" the universe?

The preposition su (which combines with l' to make sull') is used when talking "on the subject of" or "about" a specific topic. While you might see pensare a (to direct your thoughts to) or pensare di (to have an opinion of), using su clearly shows you are talking on the broad topic of the universe.

Why isn't esprimere conjugated to match the "I" doing the action?

Because it follows voglio (I want), which is a modal verb. When you express wanting, being able, or needing to do an action, you only conjugate the first verb (voglio) and leave the second verb in its infinitive dictionary form (esprimere).