Logic Gate, negative voltage
1) 0 and 1 are just to make things easy for humans.

You could also call a certain voltage range False and another one True.

You could even call them Bert and Ernie if you like but that's confusing for humans, also 0 and 1 is more compact to write down.

In the same way, if you wanted a circuit where + 5 V is 0 (zero) and 0 V is 1 (One) then be my guest. It's just a naming convention. The transistors don't care either.

2) A circuit with a +12 V and a 0 V (ground) has +12 V just because it was chosen to be like that. You could also connect that + 12 V node to ground instead but now, since it's ground, we don't refer to it as +12 V anymore because that is confusing. Now we call it ground and then the node that was previously ground is now called - 12 V

In this circuit the traditional 1 (one) would be 0 Volt and the traditional 0 (zero) would be -12 V.

In the early days of logic chips some used a common positive so all voltages in the circuit were negative ! A bit confusing now since almost no one does that anymore but it is possible nonetheless. Ground is just a reference the designer chooses.