Debbie, I can assure you he remembers you as they don't easily forget someone. Thanks so much for taking him into your home when you realized your brother wasn't giving him what he needs. It will take time for him to get over not seeing your mum any longer but it sounds like he really likes you a lot.
They drink some but not a whole lot of water, if you have provided him with a source of water he will drink what he needs, just make sure it is clean and change it often.
Why don't you go ahead and allow him to come out of the cage on his own, since he is already familiar with you he should do just fine and don't be nervous or he will sense it, just relax and enjoy Gizmo.
I would love to see some pictures of him if you have some you would share with us.