1: Tolkien’s works don’t really feature “magic items”, like you might be used to from modern games. There’s no line drawn between “these items are nonmagical but really well-crafted, but these other items are magical”. Most of what ends up getting called “magical” by ignorant folks is what the makers of those things would call “high craft”.
2: As to specific weapons: The swords that Sam, Merry, and Pippen wield are better than ordinary swords. When Merry uses his against the Witch-King, it’s destroyed just like any weapon would be, but that’s literally the highest purpose for which that sword was created, and so it’s able to penetrate the Witch-King’s magic, making him vulnerable to Eowyn’s killing stroke.
On the other hand, Sam’s matching sword was all but useless against Shelob’s webs (it took something like a half-dozen strokes to cut a single strand), but Sting slashed through them like they were ordinary cobwebs. So in that regard, at least, and possibly in other unspecified ways, Sting was superior.
Both Sting and Orcrist glow in the presence of orcs, but it’s implied that Orcrist is the superior weapon (at the very least, it’s already well-known and named, but Bilbo has to name Sting himself, because none of its specific history is known).
Glamdring is certainly superior to Orcrist: It was originally the personal weapon of the King of Gondolin, the most powerful of the ancient Elven kingdoms. And it glows in the presence of all enemies, not just orcs. On the other hand, the Orcs regarded both swords with equal dread, which suggests that Orcrist might be especially effective against them specifically.
Anduril (renamed Narsil when it’s reforged) might be on a par with Glamdring. But its main significance is that it marks Aragorn, its wielder, as the true legitimate King. That means something, to Tolkien.
3: That particular entrance to Moria (there were many) bordered on Elvish lands. The password was a relic of a happier time, when relations between the two nations were friendly, and there were few or none of the evil creatures about. The door was more about keeping out inclement weather than enemies, and so no real security was needed. The inscription of “speak, friend, and enter” was the equivalent of a sign saying “push here to open door”.
5: Treebeard is the oldest creature under the Sun, but there are those around who are older than the Sun: Galadriel, in particular, was born in the Years of the Trees. Shelob was spawned some time after her dam, Ungoliant, left the West, and therefore after the Years of the Trees, but it’s unknown whether she was before or after the Sun. Tom Bombadil, it’s very difficult to say anything about, but I think he’s as old as the World. Gandalf, Saruman, Sauron, and the Balrog might be young in their current forms, but in essence, all predate the World, and in fact played a part in its creation. Elrond, by comparison, is a youngster, born at the very tail end of the First Age.
Or to put them in order from oldest to youngest:
Illuvatar (the One, the Creator, God Almighty)
The various Maiar and Valar (Gandalf, Saruman, Sauron, the Balrog, Melian, Elbereth, Melkor, etc.)
The World, and probably Tom Bombadil with it (or maybe not, who knows)
Ungoliant
Cirdan (the elf who waits at the Grey Havens, and builds the ships: He’s of the First Generation)
Galadriel (of the Second Generation of elves)
Treebeard
Shelob (or possibly ahead of Treebeard)
Young elves like Elrond, Thranduil (Legolas’ father), etc.
Legolas
Most Dwarves
Bilbo
Aragorn
All other humans and hobbits