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 Finding 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.
The T-800 says "Come with me if you want to live" when he first meets Sarah. This is likely because John knew full well that his younger self would want to save his mother, but she would be terrified of seeing a Terminator again, so during the reprogramming he set the T-800 to say the first thing that Kyle said to her, making it easier for her to believe this one was on her side.