Learn French: Est-ce qu'ils veulent apprendre l'anglais ?

No, the -ent ending for the "they" form (ils or elles) of verbs is completely silent in French. You pronounce veulent like "vull" (roughly rhyming with the vowel sound in the English word "pull" or "sir").

Do I need a word for "to" between veulent and apprendre?

No extra word is needed! The verb vouloir (to want) connects directly to the next verb. Since the dictionary form (infinitive) apprendre already means "to learn", you just put them right next to each other: veulent apprendre.

Why is apprendre used here instead of a conjugated form?

When you have two verbs acting together in French, only the first one is conjugated to match the subject (ils veulent). The second verb stays in its unconjugated infinitive form (apprendre). This works just like English: "they want" (conjugated) + "to learn" (infinitive).

Why is it qu'ils instead of que ils?

The phrase to ask a question is Est-ce que, but in French, two vowel sounds generally don't like to bump into each other. Because the pronoun ils starts with a vowel, the que drops its "e" and uses an apostrophe to become qu'ils. This makes the sentence flow more smoothly.