The questions were intrusive, but the company wanted to gauge if you had ties, and would stay with the company.
Career driven because you are single - they are afraid you may meet a man and may relocate & leave your job
If you live at home/rent - they think you may be afraid to take a risk and buy your own house. They could think you are 'bad with money' and not able to save. They could also think you spend weekends getting pissed and are fit for nothing on Monday morning
Also, if you live at home, they may try to get away with paying you a low salary, as you wouldn't have household bills.
If you have a house - good, because you have to work to pay your mortgage, and will stay in your job, be committed etc
If you are married/partnered - good, because you won't have a holiday romance and leave your job to be with your new love.
When I was being made redundant from a job a few years ago, they gave us CV/ interview coaching. I had always put 'single' and my age on my CV. (I was about 30 then). The career coach told me not to put my marital status on my CV, as the interviewer could think 'single people have no ties, and may move jobs more readily than marrieds'. In fact, I would have thought it good to say that I'm single, as I wouldn't be taking time out on maternity leave with babies.