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:
If you rolled a 20 on the die (a "natural 20"), your result is one degree of success better than it would be by numbers alone. If you roll a 1 on the d20 (a "natural 1"), your result is one degree worse.
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.
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.
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.