House
A "house" is essentially a container -- for a person, a family, several families or even a large group with shared interests (think of the term "houses of worship.") In the Bible, a "house" is also a container, but for spiritual things rather than natural things. In various uses a "house" can represent part of the mind, the whole mind, a whole person or even a church. The other nuance to the word "house" is that it is generally used in regards to our affections and desires rather than our thoughts and principles. This makes sense; we tend to engage our thoughts and rationality when we are out in the world doing our work, but when we are inside our houses we are driven most by love for our families and the desire to be good to those we love. So "house" tends to represent the things we want and care about -- which are ultimately the things that define us.
Arcana Coelestia # 3997
3997. 'And my righteousness will answer for me' means the Divine holiness which He possessed. This is clear from the meaning of 'righteousness' as that which has regard to good, dealt with in 612, 2235. But when used of the Lord, as it is here, Divine holiness is meant, for all spiritual or celestial good proceeds from the Lord's Holy Divine.