Almighty Arceus:
Well personally I never saw Arceus giving the player access to its full power. Actually
Norne brings up Lovecratfian lore and that has something about its eldritch abominations (EA) creatures which I think would perfectly fit with Arceus. A big thing about Lovecraftian lore is that the EA aren't what anyone can "see" of them (or at least see without going insane, but that's beyond the point). The EA are essentially formless having more than just the 3 spacial dimensions of height, length, and width. Infact some of them create an avatar they control like a puppet which mortals can see without going insane and at the same time the EA can channel its power through to do what they want. And I think (or at least like to think) that's what Arceus is, a formless and infinitely powerful EA who has created an avatar which it channels a tiny bit of its power through to communicate with us mortals.
Why does Arceus let the player catch its mortal avatar? The player has proven themselves as an intriguing person who's able to form incredibly strong bonds with Arceus's children, the Pokemon species. It wants to observe the player and entices them to let the player catch it by giving them use the power which Arcues has initially given its avatar (and if need be Arceus can further limit or strengthen the avatar's power). Being its just an avatar the true Arceus is free to do what it needs to, the player is still a human so only has about a century to live which comparatively to Arceus is just a blink of the eye (if even that long), and finally Arceus can probably create a new avatar if it needs something done down at that level. That could also explain why Arceus only creates one of the Spacetime Dragon for the player in HGSS, it wanted to present the unique character with a gift that it could do so using the power of the pedestal in the Sinjoh Ruins, but only one because they don't want to make the player too powerful (I always took what Arcues was doing in that event as it using the pedestal's power to create and then destroy a micro universe so that it could create another spacetime dragon without it having it chained down to a universe (and maybe showing off its power, oh, and also what sort of forces generally goes into making a Pokemon egg)).
Why is Arceus's avatar BST just 720? Well at the time it created the avatar it was the most powerful Pokemon we've ever seen and still is for non-Mega Pokemon (which as
Vader_the_White pointed out is another timeline, but we'll get to that). As for the Unova Original Dragon being as strong as Arcues, I imagine that's a special circumstance or maybe even an experiment on Arceus's part to allow a Pokemon use the boundless power that comes from human ambitions (though it probably didn't see it splitting itself apart, but hey that's what experiments are for). At most I would say maybe Arceus allowed/capped the Unova Original Dragon's power at 720 because it was still skeptical it mortals could take a physical being with any more power.
What about the Arceus avatar in the Mega Universe? When the Sinnoh remakes come around I can't see how they'll give up a chance to give Arcues, or rather the Arceus avatar, a Mega Evolution. I'd imagine its basically the player unleashing ALL the power that Arceus had put into its avatar though since its a temporary power-up and other Pokemon are given access to this power (and making some stronger than Arceus) it'll allow that so once again it could be the strongest Pokemon (BST of 820); it could also be an experiment on Arceus's part to see if mortals could take physical beings with much higher power.
But if Arceus is so powerful what about people worshiping Rayquaza, it being taken out by a meteor, etc.? For the worship of other deity-like Pokemon that's probably people just being people. The Draconians worshiped Rayquaza because it save them and all of Hoenn by using the power of the people's prayers, thus the people not only say it as a powerful Pokemon but also as "part of" Rayquaza as they can help it achieve even more power. The Unova Original Dragon used the power of human ambitions which was eventually split into Reshiram's "Truth" and Zekrom's "Ideal" so once again people feel a strong connection to it. As for the people of Sinnoh, only they seem to worship Arceus because that's where Arceus first set up shop so its where there's the most evidence of "Arceus" as well as its first few creations (the Spacetime Dragons and the Lake Gaurdians). People not only worship what's the most powerful thing they know of but also what they feel they have a closer relationship to, just because its revealed another region has a creature just as strong or stronger doesn't mean they'll just drop their religion and start worshiping the new stronger one.
Also remember the anime isn't made by the exact same people who make the games. As
pika pal pointed out, its taken out by a meteor yet can take on all 3 Spacetime Dragons? I suppose if you put in my theory into effect that maybe at that time the Arcues avatar underestimated the meteor's strength and ended up badly injuring itself. It was dying, though had it died the actual Arceus could have just created another one but luckily Damos saved it. Flash forward to the Arceus avatar waking up after having been betrayed, Arceus is P1$$3D and so is no longer holding back. Its unleashing ALL its power so it can easily take on the Spacetime Dragons.
Mewtwo's Origin:
Hmm, while I wouldn't say other Mewtwo weren't made I think only one was made in Kanto by Dr. Fuji. How I see it, an organization (be it Team Rocket or another) decided they wanted THE (one) ultimate Pokemon so got a group of scientist together to do so, one being Dr. Fuji who I'm guessing from his importance in the story probably was the lead scientist. Deciding to base it on Mew who's DNA is easily manipulable, they find a piece of Mew DNA (probably on Faraway Island, thus why the sign was written by Mr. Fuji) and started work on cloning their ultimate weapon. They succeed but it was too powerful and it escaped (going to Cerulean Cave/Kanto's Unknown Dungeon), after so the scientists disbanded. Now we know that Dr. Fuji probably retired after the incident, probably feeling horrible they made such a destructive Pokemon, and went to Lavendar Town and started running the Volunteer Pokemon House. But what about the other scientists? I wouldn't be surprised if some of them probably were shady and went to work for other organizations with the promise of making them their own ultimate Pokemon (probably also having a bit of Mew's/Mewtwo's DNA and data on the creation process). Obviously there is still a limited about of Mewtwo, kind of defeats the purpose of an "ultimate" weapon to have a lot of them running around, but that would explain why there are Mewtwo elsewhere.
I also standby my theory that, though incredibly rare and probably non-existent, there is such a thing as a natural Mewtwo. Mew was created probably by Arceus to populate the Pokemon World with a variety of species which Mew would evolve into (thus why Mew had DNA of "every" Pokemon, in actuality every Pokemon has DNA from a Mew). Depending on the environment Mew evolved into Pokemon species that would thrive there. This was when the Pokemon World as first forming, nowadays the world is filled with Pokemon and the Mew who are left no longer need to evolve into other Pokemon. However they still have that trigger inside of them and I wouldn't be surprised if that trigger could activate due to a flaw or accident and the Mew, now evolving without any environmental stimulus to shape its evolution, evolves like a Pokemon would into a stronger form of itself: Mewtwo. Of course being how rare Mew is and this would be a rare condition it probably hasn't happened more than once. Why do I say once? Because in Pokemon Ranger: Guardian Signs (which is canon like all other Pokemon Ranger games) there is a Mewtwo who was in hyperbolic sleep on board the Dark Fortress and I think it was said by the Sociatea it was there when the got there (and being the last time the Dark Fortress was used in ancient times before modern science, that would mean either a natural Mewtwo existed in ancient times or maybe a Mew was put in there and over the years in hibernation the evolution triggered and it became a Mewtwo).
Mega Stone Origins:
However I do agree with you on the Mega Stones. Mega Stones are just stones which just so happen to match certain Pokemon's signature/essence/aura/wavelength/whatever and that Pokemon can use it to Mega Evolve. The stones weren't specially made for the Pokemon, the stone was just radiated with Infinity Energy (the energy that the Ultimate Weapon used and later Mr. Stone was able to replicate). And it just so happens there are stones which react to Mewtwo. I suppose it could also be possible over time the Mega Stones could absorb the essence of Pokemon living and change so they become Mega Stones for that Pokemon, so maybe there wasn't Mega Stones for Mewtwo originally but when some came into existence a few stones were effected by them and eventually changed into Mewtwonites.