So Rule Zero is what allows a DM to make rulings that then, due to the precedent thus set, become house rules for that campaign.
Again, you are overlooking the critical distinction: The former is a paperjam-clearing tool that ensures smooth future operation. The latter is actually
creating something new. The two are distinct things. One is not creating anything, just jiggling stuff enough to keep things moving. The other is actually declaring something new.
Using a plunger to unclog a toilet isn't
changing the toilet in any way. It's just dealing with a temporary blockage. Redoing the plumbing because you want to add or remove a bidet from the toilet is a completely different thing.
Hypothetical example: Magic Missile can only target a creature, so what happens if someone casts one when there's no other creatures around? Does the caster have to shoot herself with her own missiles? Can she just fire them into the ground? If yes, do they have any effect on the ground e.g. char marks or chipped stones etc.?
Except there isn't any ambiguity here--not in the rules themselves at least. If you do not have a valid target for a spell, the rules are explicit that you can't cast it. You might decide you don't like that rule, but there is a difference between "this is genuinely unexplained/conflicting/ridiculous" and "the rules are clear, explicit, and reasonable, I would just prefer that they said something other than what they say."
That said, you (almost) always have a valid target for the
magic missile spell, because it isn't friendly. You, yourself, are a creature you can see. So unless you're invisible and also lack the ability to see invisible things (e.g.
truesight), there always is a target for the spell:
you. Thus, if "successfully" cast while no other creatures are present, all of the darts hit yourself, because you are the only creature you can see within range. Since I sincerely doubt the player
wants that, the reasonable choice is to tell them they can't cast the spell if there are no creatures they can see and would choose to target within range.
Rule Zero allows me-as-DM to rule on the fly that untargeted Magic Missiles can be fired into the ground, with each missile possibly leaving a small char mark where it hits.
As noted, this is not "Rule Zero," because you are straight-up
rewriting the spell, not just adjudicating an ambiguous statement, rules lacuna, or ridiculous incongruity.
That ruling sets a precedent for the campaign - now that I've ruled one Magic Missile works this way, that's how they'll all work henceforth - and so I put it into the spell write-up as a house rule.
You were already writing a house rule before you even started: you decided you didn't like the "target" line of the
magic missile spell, and wanted to rewrite it to "one creature
or location of your choice that you can see within range."
No, as stated.
I think it's the other way around: house rules are a subset of homebrew. With house rules, you're just tweaking what's there while leaving the root system pretty much intact. With homebrew, you're adding or removing or kitbashing or (re-)designing core elements of the root system and-or setting.
Not at all. House rules may have nothing to do with creating your own content. A casino can have house rules defining when and how a player is allowed to cash out, without touching in any way the rules of the games of chance that it offers. A DM may require that everyone roll for their stats, forbid any form of multiclassing and all feats, and mandate that players only choose human, elf, half-elf, dwarf, and halfling for races. None of that involves even the slightest creation of new content. Homebrew, by its very definition--
brewing something up--is specifically the creation of new or rewritten content. Hence, homebrew is necessarily a rule specific to only those tables that use it--a rule specific to that "house" in the same way as one refers to a casino as "the house"--but a house rule need not in any way create or modify the actual content of the game.