Option 1 is the correct answer here
Ability checks always add up d20 + ability modifier + situational modifiers, as long as this is greater or equal to the DC then you succeed at the task. This applies to all ability checks for all ability scores.
In terms of a natural 20, this is entirely up to your DM from what I can find. For the group that I DM I allow success on the task if it seems fairly reasonable, but for instance a player trying to punch through a dungeon wall would never succeed with fists alone (without special fists too).
Generally if the task is impossible, the DM should directly say that you make the attempt and fail, no roll necessary.
Do all opposing skill checks automatically succeed on a natural 20 (
unless there's a tie )?
No, but it's pretty hard for an opponent to beat a natural 20. The opposing roll only ever wins if its total check is higher despite the natural 20. This may happen, say, when a player has a negative modifier to a roll and the opponent rolls high and/or has high scores in the opposing roll.
In one of our games, my 8 strength Lore Bard beat our 18 strength fighter in an arm-wrestling, basically a Strength(Athletics) contest, by picking up Expertise in Athletics, throwing insults at him (Cutting Words Lore Bard feature), and cheating (casting Enhance Ability on myself).
If not all opposing skill checks automatically succeed on a natural
20, do any of them? If so, which ones?
Ability Checks don't have critical success unless house-ruled into your game but I'd be wary of this and that's another topic entirely.
Besides saves & attack rolls, what treats a natural 20 as an automatic
success?
Only Attack Rolls treats a natural 20 as a critical hit, even if you roll a natural 20 on a Wisdom Saving Throw, you're still going to be frightened of that dragon if the total doesn't equal or surpass the Save DC.
Best Answer
They do not, and for very good reason
A twenty-sided die has a 5% chance, each, of rolling a 1 or a 20. That is a very high chance relative to some of the things you can attempt to do with skills. A 5% chance of automatic failure or automatic success simply is not appropriate to the things that skills are used for.
A particularly good example is the Acrobatics skill, when used to jump. The DC for any given jump you wish to undertake is equal to its distance; if you succeed on the check, you land where you want, but if you fail you fall short. But what if you say “I attempt to jump to the Moon” and then roll a natural 20? If a natural 20 was an automatic success, then you would then jump to the moon. Obviously, that’s not a good thing for the rules to allow.
That’s a pretty extreme example, but for the most part, that’s how skills work: you should not be able to succeed on checks that are greater than 20 + your bonus, nor should you ever fail things that are less than your bonus (because you are thus extremely skilled in that thing, or it is extremely simple, and in either case a 5% chance of failure is just too large).
Use Magic Device
This is a special case that a lot of people read quickly and think is a weird exception where a natural-1 on a skill check automatically fails. Read the sentence carefully: the statement is that you cannot retry if both of the following are true:
You roll a natural-1.
You fail the check.
If your natural-1 is sufficient to meet the DC, you succeed, and are not limited in using the item in the future (at least as normal for that item; if it’s out of charges or whatever, that would stop you). You only have a problem if your natural-1 is insufficient to meet the DC.
Note that scroll mishaps occur in the same circumstance (natural-1 that fails).