When did rhyme enter Latin poetry or song?

1. Did Latin poetry rhyme?
2. What are the forms of Latin poetry?

Did Latin poetry rhyme?

it's true that, because Latin is an inflected language and has a lot of freedom with word order, Latin poets tend to avoid rhyming.

What are the forms of Latin poetry?

There are four basic families of verse: dactylic, iambic (and trochaic), Aeolic, and anapestic.