Learn French: Chacun doit installer le programme sur l'ordinateur. - Each one must install the program on the computer.

Chaque is an adjective, which means it must always be followed by a noun, like chaque personne (each person). Chacun is a pronoun meaning 'each one,' so it stands alone as the subject of the sentence without needing a noun after it.

Could we use the feminine form chacune in this sentence?

Yes, but only if you are specifically talking about a group of women or feminine nouns. When referring to a general, unspecified group of people, or a mixed-gender group, French always defaults to the masculine chacun.

Since chacun refers to everyone, why do we use the singular verb doit instead of the plural doivent?

Even though chacun applies to everyone in a group, it literally means 'each one'. Because it focuses on the individuals one by one, it always takes a third-person singular verb, exactly like il or elle.

Why is installer left in its infinitive form instead of being conjugated?

This is a standard French rule: when two verbs are used together, the first verb is conjugated and the second verb stays in the infinitive. Here, the modal verb doit is conjugated, so the main action verb installer remains unconjugated.