Let's say my character Strikes an enemy with AC 35. My attack bonus is only +10.
I roll a natural 20, making my total 30 vs his 35 AC. Is this attack treated as a regular hit, because it would have been a failure but the nat 20 improves the degree of success by one step? Or is it treated as a critical hit, because it's a nat 20?
Similarly, if I'm subjected to a spell with a saving throw I can only fail at, and I roll a nat 20, does that mean I reach a success on the saving throw or a critical success?
Best Answer
In General
Chapter 9: Playing the Game (Core Rules) describes how criticals work. As you noted, a critical success and failures occur when your result is the DC +/- 10. You seem to misunderstanding how rolling a natural 20 works. From page 445:
A natural 20 is not a critical hit. A natural 1 is not a critical failure. They only modify what your result would have been by one step.
Your Examples
In your first example (a strike against a DC 35), you have a success. Your result of 30 would normally be a failure, but since it is a natural 20 it becomes a success.
The second example works the same. If you would have failed your saving throw, that natural 20 makes it a success. If it would have been a critical failure, then it now becomes a failure instead.
About Attacks...
The current printings of the Core Rulebook do have a different section which addresses critical success on attacks. These are on page 278 (in the Weapons section). Under these rules, a natural 20 is a critical success on an attack.
However, as this answer on another question on the same rule points out, Paizo announced at PaizoCon their intent to errata this rule away as it was an error.