Learn Russian: Возраст — это не проблема.

In Russian, the present tense of the verb "to be" (is/am/are) is usually skipped. When linking two nouns, like "Age" and "problem", Russian writers use a long dash to replace "is". The word это (this/it) is often added right after the dash to make the sentence flow better, so it literally reads as "Age — this is not a problem."

This lesson is about using the Dative case for age. Why is возраст in the Nominative (dictionary) case here?

You use the Dative case when expressing how old someone is (e.g., Мне 20 лет literally means "To me are 20 years"). But here, you aren't saying how old someone is. The word возраст (age) is just the main subject of the sentence doing the action (being not a problem). The subject of a sentence always takes the Nominative case.

Why is it не проблема instead of нет проблема?

Не means "not" and negates the specific word that follows it (not a problem). Нет means "no" (as the opposite of "yes") or is used to say that something doesn't exist ("there is no..."). Since you are describing what age is not, you use не.

Проблема is a feminine word. Why do we use the neuter word это here instead of эта?