Learn Hardcore Korean: konseoteu pyoreul modu sasseoyo.

Because 사다 is a transitive verb that takes a direct object. The direct object is marked with the particle -를 (or -을), not -가, which marks the subject. So 표를 샀어요 correctly means “bought the ticket.”

What role does 모두 play here?

모두 means “all” or “every.” It indicates you bought all of the concert tickets. It directly modifies the object 표. In more casual speech, you can also use 다:
콘서트 표를 다 샀어요 has the same meaning.

Where is the subject in 콘서트 표를 모두 샀어요?

Korean often omits the subject when it’s understood. Here, the implied subject is 저 (I) or 우리가 (we). If you wanted to include it, you could say (제가) 콘서트 표를 모두 샀어요: “I bought all the concert tickets.”

Why is the verb ending 샀어요 used?

샀어요 is the polite past-tense form of 사다 (to buy) using the -아/어요 conjugation. It’s suitable for everyday polite conversation. For casual speech you’d use 샀어, and for very formal situations 샀습니다.

Can 모두 be placed in a different position?