The T-800 says that his chip got set to "read-only" before he set off on his mission. If he can't form any new memories, he'd be about as effective a killer as Dory from Saving Nemo.
The chip isn't his memory storage; it's more like his OS and Drivers. It's set to Read-Only so that it doesn't change and adapt. He's recording and remembering things constantly, he just isn't learning from them.
The reason Sarah, John and "Uncle Bob" can get supplies at "Cactus Jack's" without attracting attention or being tracked is John had just swiped $300 from the ATM before.