Can I cast Passwall under an enemy to drop them into a 20-foot pit?
If so, does said enemy get any saving throw to avoid the effect?
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The passwall spell description says:
A passage appears at a point of your choice that you can see on a wooden, plaster, or stone surface (such as a wall, a ceiling, or a floor) within range, and lasts for the duration. You choose the opening's dimensions: up to 5 feet wide, 8 feet tall, and 20 feet deep. The passage creates no instability in a structure surrounding it.
When the opening disappears, any creatures or objects still in the passage created by the spell are safely ejected to an unoccupied space nearest to the surface on which you cast the spell.
The spell description does state that a floor is a valid target, as long as it's a wooden, plaster, or stone surface. And as you note, the passage can be up to 5 feet in one dimension, 8 feet in the other, and 20 feet deep - so it can create a pit that's 20 feet deep.
The spell doesn't specify whether any enemy standing on such a floor gets a saving throw to avoid falling... So if spells do what they say they do, the creature arguably falls instantly without a saving throw (assuming they aren't flying or hovering). Of course, the spell doesn't address this possibility specifically, so a DM could easily house-rule otherwise.
However, this can't be used to permanently trap the enemy that falls in; after an hour (the spell's duration), as the description states, any creature still in the passage is safely ejected to an unoccupied space near the surface on which the spell was cast (so, the floor above) and the passage goes away. Thus, while the spell could inconvenience the enemy for up to an hour, they are free to do as they wish afterwards. The only way to trap them like this would be to cast it such that they fall into an enclosed space 20 feet or less beneath the floor.
Yes, I think that Passwall could be used to tunnel or dig into a space that doesn't reach an opening on the other side (ie. hillside or ground).
However, 20 feet of falling damage to one or two opponents may not be the most effective use of the spell. They may be able to climb out or escape relatively quickly and the one hour duration will eventually return them harmlessly to the surface.
Depending on your environment, such as in a castle or fortress for example, you don't need to make a 20 foot pit. If you're not on the bottom level, you could essentially remove a 5x20 or 8x20 section of a hallway floor (only 8 or 5 feet deep, thicker than the floor should be), dropping your opponents to the level below and then end the spell effect, restoring the floor/ceiling above them.
This application may not damage or immobilize your targets, but it should at least remove them from combat until they are able to find you again.
Spells do what they say, no more, no less.
The passage created by Passwall is
The spell reads:
You choose the opening's dimensions: up to 5 feet wide, 8 feet tall, and 20 feet deep
These are restrictions on the passage. For normal use, the height of a passwall tunnel and its depth are in different direction.
For a "pit", depth and height end up aligning.
When you build one going down, both the depth and the height are restrictions on how far down it can go.
Similarly, the width is limited to 5'; so you can use passwall to create a 5' by 5' by 8' pit.
A 20' pit would be allowed by "20 feet deep", but it would be more than "8 feet tall", so isn't allowed by the full restrictions of the spell.
There is no saving throw against this effect, because spells do what they say and no more.
As you take 1d6 damage for every 10', this pit does 0 damage. It is a bit annoying to climb out, especially for small foes.
You could use it quite effectively on a bridge that is less than 8' thick; the target would fall through the bridge with no saving throw.
Several things occur to me from a lengthy amount of time playing D&D (about 15 years starting in the mid-1970s on "tabletop" and continuing electronically today).
The GM/DM (or whatever) is the ultimate adjudicator in the use of spells, but they are normally considered to do what they say - which means in the case of a Passwall: Yes, they can make a hole in the floor. However...
When applied to the floor, the dimensions would remain being transfigured to the "new plane" as a hole "up to 5 feet wide" (approx 18 inches to either side of your (character's) body and 8 feet long (the "new plane's" conversion of tall) and 20 feet deep (which means deep in any direction the resultant hole is facing), thus causing 2d6 of falling damage to anyone who falls in, plus (possible) crushing damage to the bottom ones if more than 2 should fall in if it is cast "in front of" charging enemies.
As for "saving throws", it would depend on the person running the campaign or scenario. The people I played with have said yes, because spells are not instantaneous; they requires voice and or hand/wand gestures (and sometimes use of ingredients) to cast, and therefore any "practiced adventurer" (over 1st level) who has seen spells cast, and especially spellcasters, would recognize that one was being cast and act to dodge away from the area it seemed to be aimed towards, or even act to counter if that is used in the particular game, and would therefore get a "Reflex Save" to see if they accomplished their chosen action in time.
And as a last "tidbit" to think about: while the hole created will spit them back out "when it ends", the spell doesn't say you can not throw "room furnishings" on top of those in the pit to help ensure not only more damage but less of a chance of them climbing out if there is enough available, such as in the "dining hall" or armory of a castle. Being "pinned" by several hundred pounds of furniture or weapons should make getting out a lot harder, if you don't care to stand around shooting "fish-in-a-barrel" while they are stuck. Or dump in a couple of barrels of oil and a torch to keep them toasty warm while you avoid any friends of theirs in the area.