So the father knew (εγνω ουν ο πατηρ). Second aorist active indicative of γινωσκω. Inferential use of ουν.

Himself believed (επιστευσεν αυτος). Not just the word of Jesus (verse John 4:50), but complete faith in Jesus himself as the Messiah, absolute use of πιστευω as in John 1:7.

And his whole house (κα η οικια αυτου). All his family, the first example of a whole family believing in Jesus like the later case of Crispus (Acts 18:8).