Learn Spanish (Spain): Mi casa tiene seis dormitorios.

No, the numbers 2 through 10 never change their endings for masculine or feminine words. Whether you are counting masculine dormitorios or feminine casas, it is always seis. Only the number one (uno, un, una) changes to match gender.

Why do we use tiene here instead of tengo?

Tiene is the form of tener (to have) used for he, she, or it. Here, the subject is Mi casa (my house), which counts as an "it". Even though the word "my" is there, you aren't the one doing the having, the house is!

Why is it mi casa and not mis casa when there are six bedrooms?

The word mi (my) only describes the noun right next to it: casa (house). Because there is only one house, you use the singular mi. It doesn't matter that the house contains multiple bedrooms. You would only use mis if you owned multiple houses (mis casas).

What is the difference between a dormitorio and a habitación?

Dormitorio specifically means a bedroom, coming from the verb dormir (to sleep). You might also hear people use habitación, which often means bedroom in everyday Spanish, but literally translates to a general room.