Tire Inflator Portable Air Compressor 12V DC Car Air Pump with Digital Display, LED Light, Auto Shut Off Function, Set of Nozzle Adaptors for Car, Motorcycle, Bicycle, Ball

Q: Why doesn't it cut on when connected?

I am not sure if this helps, but you need to make sure car power is on. It won't turn on unless it's getting power from the car. I haven't had any issues with it turning on if it's securely connected and the car battery is on.

Q: Will it show your tire's current psi without having to preset the psi first?

Yes, it will show your tire's current psi

Q: Any warranty and if so who honors it you or the the manufacturer?

There is supposed to be one. There was a QR code that you can use. When I put it in my phone it did not work. I figured that the product did not cost much so that I would use it until it died.