Learn Spanish (Latin America): Necesito cien dólares o doscientos pesos. - I need one hundred dollars or two hundred pesos.

No, you must use cien when you have exactly 100 of something. You only use ciento when the number is over 100, such as in ciento un dólares (101 dollars).

Why does doscientos end in -os?

The hundreds from 200 to 999 change their endings to match the gender of the noun they are counting. Because pesos is masculine, we use doscientos. If we were counting a feminine noun like monedas (coins), we would say doscientas monedas.

I remember dólar has an accent mark. Why does the plural dólares still have one?

In dólar, the accent tells you to stress the first syllable. When you add -es to make it plural, the word gets an extra syllable. The written accent stays on the o in dólares so you know to keep stressing that exact same syllable.