Learn Dutch: We hebben elkaar veel te vertellen. - We have a lot to tell each other.

It expresses having a task or possessing something that requires action. Here, hebben combines with te vertellen to mean "have to tell". It works very similarly to English, indicating that we have something (news or stories) that we need to share.

Why is elkaar placed before veel?

In Dutch word order, the indirect object usually comes before the direct object. Here, elkaar (each other) is the indirect object receiving the action, and veel (a lot) acts as the direct object. So the literal order is "We have each other a lot to tell."

Could I use moeten here instead of hebben ... te?

You could say We moeten elkaar veel vertellen, but it slightly changes the feel. moeten implies a strict obligation (We must tell each other a lot), whereas hebben ... te vertellen simply means you possess a lot of information that is meant to be shared.

Is elkaar the only word for "each other" in Dutch?

elkaar is the standard word you will use most of the time. You might also hear Dutch speakers say mekaar, which means exactly the same thing but is highly informal and mostly used in spoken language.