In the Transdimensional arc, with Bill temporarily sealed away, does that mean other demons are fighting each other or trying to take Gravity Falls as their territory with this chance, with it rising when the “new” demon, Alcor appears out of nowhere?

Probably not; this is a world that is PRE transcendence, and while demons can be summoned, they’re not as out in the open or as easy to reach as they are in the main TAUverse

For reason aside from both Dipper and Alcor being snarky, salty (and a teasing troll on Alcor’s part) to each other in the transdimensional arc, I can’t help but find an interesting in-depth character analysis between these two and their interactions. Dipper can’t deny the fact that Alcor IS him, since he himself does have a vindictive streak, only Alcor just shows that he doesn’t hold back on that and it terrifies him that he could be like him and lose his morals.

One of things I enjoy from the Transdimensional arcs is Dipper learning who Alcor really is and having thoughts on the fact an alternate self became a demon and have that demon envying Dipper because his future is still open and he won’t suffer the lost of his humanity like him.

Transdimensional arc: When the agents get involved, they are after the same thing as in NWHS and ATOTS, but in addition in taking Stan’s into custody, they also take Tyrone (Alcor) into questioning since they dig stuff up and know that a Tyrone Pines never existed and he doesn’t have any existing records. So they suspect he may be Stan’s accomplice or may be something else or related to the paranormal activities they’ve observed.

Not to mention there’s something about this Tyrone character that makes the hackles rise up on Agent Trigger’s neck.

He’s going to get to the bottom of this, one way or another.

During the transdimensional arc, Alcor would often “spoil” the true nature of the attractions in the Mystery Shack, from true origins of each material used and how it was made to how the work was created.

At least until Stan chased him out of the Shack with a holy water spray bottle.

In the transdimensional arc, both Dipper and Stan will learn that whenever Alcor annoys them or trolls them, one of the ways to get back at him is the same way Henry deals with him whenever he does those things- the broom.

Stan finds out about this first. It’s completely accidental, pure reflex, but it works.

Then it becomes deliberate.

I know there’s a fic in the transdimensional arc that has Alcor trolling Gideon when he accidentally summoned him, but shouldn’t he be careful since that might come back to bite him later on?

On the one hand, caution; on the other, chaos.

Sometimes people do reckless-in-hindsight things because they seem like the most fun at the time, and Alcor does what Alcor does. 🙂

In the transdimensional arc, would anyone note the similarities with Dipper and his strange but dorky “older cousin” Tyrone?

Sure, but there honestly comes a point where everything just falls under “ah, I see the family resemblance” and it’s left at that. Trust me, nobody’s going to be looking that closely or caring that much. This is not to mention the fact that Alcor’s physical body is magically fabricated, and his appearance is therefore moderately malleable – he may or may not have exactly the same features aged up, and aging does make things look different anyhow.

Basically, no, nobody is going to look at the two of them and deduce that one is clearly the older version of the other, having traveled across dimensions and time. Sometimes a small handful of shared genetics just come through strong, and most people have better things to direct their attention towards.

During the transdimensional arc, how come Alcor’s arrival doesn’t risk a time paradox? And would his presence in this presence have some territorial creatures preserve him as a threat to their turf?

Quite simply because he’s traveled to an alternate dimension which happens to be roughly analogous to the past of his own dimension. He’s not changing his own past – all he’s doing is changing their future. The dimensions remain ever separate in terms of actual timeline, so there is no paradox.

As for bugging things by turning up, it’s possible – Bill certainly wasn’t happy with it, to say the least.

So what is the Gravity Falls like in the transdimensional arc? Is the town still active despite the looming threat and monsters, like tourists and visitors entering and leaving the town like always? Like despite the shack being the only safe place, people still hang around outside of the safe place?

The Gravity Falls of the Transdimensional arc is pretty much just like the Gravity Falls of the show canon pre-Weirdmageddon. Sure, odd things happen sometimes, but it’s not like the apocalypse. The Shack isn’t some kind of sole bastion against a dangerous world. Things are fine.