HA if the home is paid for or if the minister is paying cash as he builds?

My husband is a qualifying minister and we normally receive HA for our current home which has a mortgage. If we sell and use our equity to build and pay for a new home would we lose our HA since we would not have a mortgage or rent?

And my second question is during the years we are building a house could we deduct the cost of building(assuming we pay cash as we go)as HA for those years until the home was finished?

I realize the amount of HA would have to be set at the beginning of each year.