Learn Spanish (Latin America): ¿Puedes pagar trece dólares, por favor?

Because it comes right after the conjugated verb puedes (can you). When you use two verbs together like this to express a single idea, the second one stays in its base form (the infinitive). Just like in English, you wouldn't say 'can you pays', you say 'can you pay' (puedes pagar).

How do I know puedes means 'can you?' as a question, rather than just the statement 'you can'?

In Spanish, you can turn a regular statement into a yes/no question just by changing your tone of voice (going up at the end) and adding the upside-down and regular question marks. The word puedes works perfectly for both 'you can' and 'can you?'.

Why does dólares have an accent mark over the 'o'?

It tells you exactly where to put the stress when saying the word out loud. When you make dólar plural by adding -es, the natural spoken stress would normally move to the next syllable. The accent mark is used to keep the strong stress locked on the o.