Ability Checks
Are attack rolls and saving throws basically specialized ability checks?. They aren't. Ability checks, attack rolls, and saving throws are all different kinds of D20 Tests that can be made during a game of D&D. As such, all three share certain similarities: rolling a d20, being affected by Advantage and Disadvantage, adding modifiers, and comparing the total to a target number. But ability checks, attack rolls, and saving throws are each distinct from the other. If something in the game affects one, such as the Guidance spell, the other two aren't affected unless the rules specifically say so. A game rule that affects D20 Tests affects all three.
Can you get a Critical Hit on an ability check?. Ability checks don't score Critical Hits. Attack rolls do.
Is a 1 on an ability check an automatic failure?. Rolling a 1 on an ability check or a saving throw is not an automatic failure. A 1 is an automatic miss for an attack roll.