Learn Farsi: سلام به خانواده!

In English, you might say "Hello family!" but in Farsi, it is very common to use "Hello to" when greeting a group or sending regards. The preposition be translates directly to "to" in this sentence.

Where is the word for "the" before khânevâdeh?

Farsi does not have a specific word for "the". The word khânevâdeh can mean "a family", "family", or "the family" depending on the context. Here, we know from the situation that we mean a specific family.

Is this something I would say when walking into my own house?

You can, but it is much more common to use this phrase when sending regards through a friend, similar to saying "Say hello to the family!" in English. If you walk into your own house, you would usually just say salâm.