Learn Dutch: Jouw moedertaal en dat dialect zijn makkelijk te leren. - Your mother tongue and that dialect are easy to learn.

In this construction, the subject of the sentence (Jouw moedertaal en dat dialect) is actually the logical object of the verb (leren). When the noun is moved to the front of the sentence like this, we only use the adjective + te + infinitive. You would only use om ... te if you restructured the sentence with a dummy subject: Het is makkelijk om jouw moedertaal te leren.

Why does the sentence use Jouw instead of the more common Je?

Jouw is the emphatic form of the possessive pronoun je (your). Using jouw places specific stress on your mother tongue, perhaps in contrast to someone else's. If you didn't want to add that emphasis, Je moedertaal would be perfectly fine.

Why is it dat dialect and not die dialect?

Dialect is a neuter noun (het dialect). For het words, the demonstrative pronouns are dit (this) and dat (that). If it were a de word, you would use deze or die.

Does the adjective makkelijk need an -e ending here because the subject is plural?