Learn French: Mon père et ma mère habitent ici. - My father and my mother live here.

In French, possessive words have to match the gender of the noun they describe, not the gender of the person speaking. Since père (father) is masculine, you use mon. Because mère (mother) is feminine, you use ma.

Can I just say mon père et mère to mean 'my father and mother'?

No, in French you cannot skip the possessive word in a list like we often do in English. You have to repeat it before every single noun. You must say mon père et ma mère (literally: my father and my mother).

Why does the verb habitent end in -ent?

The subject of the sentence is two people (mon père et ma mère). This means we are talking about 'them', which is the ils/elles plural form. For regular -er verbs like habiter (to live), the 'they' form always ends in -ent.

How do I pronounce the -ent at the end of habitent?

You don't! The -ent ending on French verbs is always completely silent. You just pronounce the word as if it stops at the letter 't'. It sounds exactly the same as the singular form habite.