Learn Dutch: Het huis van mijn oma is klein. - My grandma's house is small.

Because it comes after the verb is. In Dutch, adjectives only get an extra -e when they are placed directly in front of the noun (like in het kleine huis). When used later in the sentence as a description, they stay in their basic form.

Is it also correct to say mijn oma's huis instead of het huis van mijn oma?

Yes, mijn oma's huis is perfectly fine and means the exact same thing. However, using van (literally: the house of my grandma) is extremely common in Dutch for showing ownership, even for people.

Since the house is small, could I use the diminutive huisje instead?

Absolutely! Dutch speakers love using diminutives for small things. You could easily say het huisje van mijn oma (my grandma's little house), which also sounds a bit more cozy and affectionate.

How do I know whether to use het or de for huis?

Huis is a neuter noun, so it always takes the definite article het. There is no strict rule for why it is neuter, so it is best to always memorize the article het together with the word huis when you learn it.