Seems a bit strange to me that he's invited you to his place for the rest of the day, you don't even know if he's telling the truth about his mum. Imo it seems a bit early meeting up after only talking for a week but whatever, I think you should meet in public and stay in public on your first meet, get to know him first, see if he's trustworthy etc.
The least you want is to go to his, find out he was lying about his mum being home, and something horrible happening.