Learn Spanish (Spain): Cien pájaros viven en el bosque. - One hundred birds live in the forest.

You use cien when you have exactly 100 of something and it comes right before the noun (like cien pájaros). The word ciento is used for numbers over 100, like 101 (ciento uno).

If the noun was feminine, would cien change to match it?

No, cien never changes to match gender. It is always cien, whether you are talking about masculine things like cien pájaros or feminine things like cien casas (one hundred houses).

What is the base form of viven?

The base form (the infinitive) is vivir (to live). Because the subject of the sentence is the birds ("they"), we drop the -ir and add the "they" ending -en, making it viven.