Nice observations. I’d add that technology is both the creator and cure of all major problems, underscored by in-universe science, and if it ever becomes about hugs, faith and love saving the day, it’s wandering too far into Who territory.

"In exploration it's the journey that makes it fun."
Spot on.

I remember having a discussion about Star Trek captains with some friends (before Discovery and even the Abrams reboots were a thing) and how they each treated rules like the Prime Directive. Our conclusions were as follows.
Kirk: Broke the rules whenever he was SURE he was right, and being the luckiest man in the universe he always was.
Picard: Broke the rules when he was sure he could persuade even the harshest critic, in writing, that he was justified, and was enough of a scholar to pull it off.
Sisko: Broke the rules whenever he felt like it, and got away with it by suppressing knowledge of what happened and working out in the galactic boonies where there was a lot less follow-up.
Janeway: Broke the rules more rarely than the rest and only when she was particularly emotional, and got away with it by being on literally the wrong side of galaxy.
Archer: There literally weren't any rules yet, his screw ups are why there are rules later.

One of my favorite moments of consistent tech is in an episode of Voyager where the main deflector fails, the ship gets shredded by microscopic space particles.

It's also important to remember that the Star Trek crew are just that - a crew - who are engaged in a job of work.  They aren't just a bunch of mates who happen to be having an adventure together,

Rule #1.5
Space Is Big, and therefore Help Isn't Coming.
The crews in Star Trek generally have to figure stuff out on their own, even though there must surely be excellent experts in the Federation (or beyond) that might have insight to their problems.

Sure, in many cases the issue of the week could be solved by a quick subspace call to Starfleet Medical, or by engaging the services of an actual lawyer, or through consulting other people who've visited such-and-such a planet, but where'd the fun be in that? Star Trek has a way of throwing the characters into uncomfortable situations that go beyond their primary role, and I think that's a defining feature of the franchise (which I must say, I love).

I would add another rule that they never really outright say but is largely understood: Almost everyone acts like mature mentally balanced adults, unless there is some compelling reason to do otherwise.

I realized this on my last STNG rewatch when I hit "The Neutral Zone" episode. That's the one where they revealed the new Romulans, and had a side plot of thawing out some cryonically frozen people from roughly our time.

The entitled rich guy had the most trouble adjusting. The telling bit is he gets in trouble for using the coms panel when he shouldn't and literally just taking the turbolift straight to the bridge. They never lock the coms panel after he uses it, Picard comes and yells at him. They don't put security on the door -- to start with or even after he misbehaves. Why? Because it never even enters their heads that a grown-assed human would even do something so out of line and immature.

Even when he gets out of line they don't do anything more than tell him it's not appropriate behavior -- expecting that to be enough to sort him out.

We all know the split we're talking about here. There are adult humans walking around who are grown-ups and there are adult humans who got older without maturing.

That's a core component as to why the Federation works. Most of its citizens are grown-ups as opposed to children who got older. Nobody is breaking stuff just because they can, nobody is starting political movements because someone's sexual habits make them feel weird. Most Federations citizens shown have a mature live and let live, curious, attitude.

Nobody is hoarding resources because daddy didn't love them. Because the available resources are so near infinitely large there's nothing remarkable about doing so. In fact it would be weird enough to prompt people to ask if you're okay and can they help you.

Instead insufficient paternal affection prompts running off to Starfleet to prove yourself, or drives you to earn the real credit of the realm: achievement and accolades.

There's still conflict because there's still plenty of other causes behind the grown-ups getting weird, especially on a starship. There's still plenty of ego-driven conflict, but it's fundamentally different from the world we live in where we have ostensibly adult people causing real harm to others for childish reasons.

“Computer: replicate a bag of mixed, precious gem stones.”

After every repeat of "Really Big," I was expecting, "You may think it's a long way down to the chemist's shop..."

I never realized Encino Man was Star Trek. You just saved billions of lives.

It needs some additional new rules:
1. No stories involving children
2. The holodeck needs an off button
3. Seatbelts should be compulsory on the bridge
4. Starfleet admirals all need to be replaced by competent people.

Rule 2: The Universe is populated by beings that can be impersonated by a Human in makeup.

8:19 I absolutely love that scene where Gillian realizes she is going to have to pick up the check and says "let me guess, they dont have money in the 24th century!" She makes that movie.

Producer Rick Berman once said (and I'm paraphrasing) to an audience of fans asking about how to get an idea or a script submitted, "Write for a period piece. That period has limitations. As long as you stick to the limitations, we'll take a look."

You could mention the "Star Trek Writers Guide" that laid out most of these rules (and some others) back at the very beginning.

Rule #12…
In the unfortunate event that a planetary crash landing becomes necessary, a PLANET will always be readily available. Additionally, the planet will always have a breathable atmosphere, along with Earth-magnitude gravity.

Gene Roddenberry had another rule: Starfleet personnel do not come to blows with each other. Writers love to create conflict to advance a plot or enable a character's growth, but Gene insisted the source of the conflict must be others outside Starfleet; Starfleet itself must always be presented as one big happy family. I would call it a bit corny if it weren't for the fact that Star Trek's enduring relevance in the world owes largely to its hopeful view of our future. The future, ST teaches consistently, will be better than the present because humans will continue to grow and learn over time.

another rule - when you see episodes about Time Travel or Holodeck, that is the production trying to save money by finding an excuse to use old period costumes collecting dust in storage.

Error: shields aren’t generated by the navigational deflector dish. The deflector dish projects a deflector beam ahead of the ship, clearing its path of particles so that the ship can safely travel at relativistic/FTL speeds.

Shields are generated by the grid lines we see covering the hull.

Rule #10 : The warp core ejection system NEVER works.