1. The keyword here is
"procedures." Any D&D-like system worthy of the "old school" moniker would have procedures, a.k.a. rules, for this sort of thing. For dungeon exploration, you can just make a mark for every ten-minute "turn" on a sheet of paper if you want to keep it simple. The real meat of the idea is that various actions have codified lengths. Searching a room (not "I look behind the curtain," but "we thoroughly search the room") takes, say, 10 minutes. Trying to force, pick or batter down a stuck or locked door - 10 minutes. Torches last, say, 60 minutes, while lanterns twice that long.
You can, of course, make it a bit more fancy if you want to. I've seen DM's make a "DM sheet" which has a few rows of cells which you can tick in as the turns pass, with each row being the lifetime of a lantern. You can also put other stuff on the same sheet, such as an area for marking down the party's marching order, and/or some sort of initiative tracker.
On the larger scale of wilderness travel, it's the same thing: procedures. The system should have rules saying that e.g. travellers on foot can travel X miles/hexes on open ground, Y hexes on moderately difficult terrain (hills, forests), and Z hexes on hard terrain (swamp, mountains). Different numbers for riders. If you have a hex map with a set scale, now you can tell how far the party can travel in a day / half a day / whatever. And then you can just have a separate sheet or booklet, or maybe just use a part of your DM's notebook, to keep track of who travels where and when throughout the campaign - this is especially vital if you're running several groups with several parties in the same world and timeline. You can also use the same notes to keep track of the movement of important NPCs, the progress of various time-sensitive events and the like.
2. The most important thing about this is to
sit down and talk about this before you begin the campaign. Make sure everyone is on the same page. PvP often happens in this context: an asshole ("disruptive player") keeps griefing the party. Does dumb shit for da lulz that gets the others in trouble, deliberately sabotages the mission, steals from party members (always shamelessly and without even trying to keep it a secret), causes friendly fire by shooting arrows or casting area-of-effect spells into melee, etc.; when the others complain he just grins and says "I'm just roleplaying my character, this is what he'd do." Then when the other players finally have enough and decide that "what
their characters would do" is slit the asshole PC's throat while he's asleep, the guy starts crying to the DM about how the others are griefing him... and the DM steps in and stops the others from "going too far."
My point is, as a DM, you have to decide where you stand on players griefing each others and taking in-character revenge for it. And it's your responsibility to communicate your stance. If your policy is that "non-lethal griefing is okay but I won't let PCs kill each other," then you should say so clearly so your prospective players can go and find a DM who sucks less.
Now, you also referred to the wider-scope question of players getting into domain management and raiding/attacking each other. I don't know how this was done back in the day, specifically, but I would note that this is a rather niche aspect of traditional D&D-style tabletop roleplaying, and is arguably closer to wargaming. (And, of course, D&D grew out of wargaming.) If you're looking for players for a long-term campaign where this might become a relevant question, I would suggest you make it clear from the outset that you intend to explore such special styles and edge cases of tabletop roleplaying.
3. Once again, you're looking for
procedures - only this time it's procedures and tried-and-true practices for generating new parts of a gameworld. There's a lot of stuff on this, far more than I'm aware of. Sine Nomine Publishing's games always have rules for this sort of thing, but I don't have much hands-on experience with them. There are also many other options.
Whatever way you do it, the most important thing is to make the players understand that they need to give you proper warning if they want to do something like that. Yes, sandboxes are great, but sitting down to play at the beginning of the session and declaring that "we want to leave the sandbox entirely and travel to another one" just does not fly. It's not an issue with sandbox gaming, it's an issue with inconsiderate players. On a related note, if you end a session with the players planning to explore the Crimson Dungeon of the Doomed Satrap, then next time they suddenly decide to do something completely fucking different (and something you haven't already developed), it's
perfectly fine to step in and say "No, guys, you
said you were going to do this, I prepared to run this. You can do this, or you can do one of those other two things you've been considering earlier and which I have worked out to a certain detail, but you
cannot throw me for such a loop and go do this thing out of the blue. I'm not ChatGPT, I'm not in the business of churning out low-quality crap at a moment's notice." This is
fine. It's not "railroading."
4. In an old-school situation, you just play it out. You have the mapper or caller tell you which way they want to go. Every turn (or whenever the procedures call for it), you roll for random encounters, and do those if they happen. One thing I've seen as an alternative, only ever to be used when the game is dragging on way too far into the night, or when something has happened in-game that prevents one or more PCs from returning with the party, is the "Dawn Patrol table." Read about it
here, and of course you can make your own. And yes, these tables should be very dangerous. The idea is that the players should be able to expect worse results from relying on the table than from being competent and recognising when to turn around and start heading out.
Specifically in large and megadungeons, this question also taps into dungeon design. Your dungeon could have certain "shortcuts" that, once found, gives the party a relatively quick and safe path of ingress/egress to lower levels. Or maybe they're hard to gain control of (in the middle of hostile territory / guarded by powerful monsters / require a specific item, magic or errand to activate, etc.), but prove very useful
once the party gains access. You could also have other, more spacially scattered bottlenecks and level changes, which might be easier to find, but make it harder to get out quickly and safely. This is something you can play with to good effect.
5. If you're starting out separate groups in completely different areas, than you're essentially running two or more completely separate campaigns, since they won't have a way of affecting each other until much later. Even more importantly, you double, triple or whatever the amount of work you need to put into creating dungeons and adventures. Start them in the same general area instead. And yes, if one party finds a certain loot in your megadungeon, the others no longer can. Sucks to be them, they should have been quicker, smarter and more diligent. Mind you, "clearing out floors" is relative. Even a dungeon area with most of the hand-placed monster groups killed would still have random encounters. Also, a good setting is dynamic and alive. You might just decide that new monsters move into the "cleared out" areas. Or maybe other factions in the dungeon take advantage of the possibility to expand their own borders. Or maybe some monsters of that faction fled but will be back later with reinforcements.
