I'll take my own shot at these questions, since I have a couple of hot takes to spread
1. What mons from above do you believe will see a spike in usage?
These four mons (mainly the first three) are pretty big winners. Zeraora, Terrakion, and Kyurem are extremely menacing breakers that always had to be wary of Dugtrio's trapping potential, but now they're a lot more free to go even more ham than they've been the past month or so.
Cinderace doesn't benefit as greatly from Duggie, but it can definitely be played much more aggressively and freely, which it appreciates for sure; it also partners well with Toxtricity to dismantle a lot of the tier's most common defensive cores.
2. Which mons do you think will be overhyped and have their usage die down after a few days/weeks?
I actually kind of disagree on the idea that Toxtricity is going to die out as sharply as suggested. Toxtricity has an extremely valuable niche in the fact that it can dismantle extremely fat cores (Corvi/Pex/Clef/Toad) singlehandedly outside of Ferrothorn, and with Pex likely going to rise, it will be even more valuable. Punk Rock Boomburst is also just an amazing midground breaking move, and something it has over Dracozolt as a Electric-typed fat breaker. However, that being said, it is by no means going to be a top tier threat due to its middling defenses and speed, but its niche will be a lot more effective now that Duggie can't threaten it on a KO.
It's worth saying that a Toxtricity + Cinderace core is extremely menacing in its own right, but now that Duggie isn't around to threaten it for just existing, it's a lot more free to wreak havoc on the tier. Hippo rising will also give it yet a more specialized niche in what it breaks as opposed to Dracozolt.
I could see Dracozolt having more of a realized niche as well, but I think it might get more mileage out of a Substitute set as opposed to a Scarfed/Banded set. Seismitoad is a giant peg in its gameplan, but it can pry apart every other fat mon in the tier, and the ability to swap its moves will be much more valuable at the current moment so it doesn't have to take as many risks (with Hustle as well). Though, it hates the new influx of Hippo use, and is inconsistent by nature due to Hustle, so I don't think it'll be as flexible of a breaker as Toxtricity and will die out a lot more sharply.
This being said, though, I do think these two Pokemon will drop off a bit later, but I can't deny that they'll be better now.
3. What mons not included above may do you think will see more usage in OU?
My Incineroar bias is gonna kick up here, but I'm gonna say it. While it had the ability to pivot out or Wisp Duggie on the switch, being able to hard switch out without worries of taking a giant, SE STAB EQ is a giant boon for it, as now it has even more flexibility as a pivot. I still hold my stance that it has a solid niche in the metagame, and now even more of one now that it can more selectively and soak hits as it needs to, and pivot accordingly.
I hate this thing.
I actually think the Screens HO playstyle has gotten better since offensive behemoths such as Zeraora/Terrakion don't have to worry about being trapped. They can much more effectively and aggressively set up without the threat of Duggie to come in abruptly, and I believe Screens will catch on to further capitalize on this offensive potential down the line. Ninetales in particular stands out to me, since it resists Kyurem's Freeze Dry/Ice Beam and outspeeds with a Moonblast/Veil, and just lets Bulk Up Zeraora clean house.
4. Aside from Arena Trap users (Dugtrio, Trapinch and Diglett), is there anything that may see less usage now that Arena Trap is banned?
Fat cores for sure have taken a giant hit from the ban. They have to watch out for offensive cores that Duggie once hard checked, because there are a lot of offensive behemoths that do a pretty great job at deconstructing them without having to worry about being trapped.
5. How do you think the metagame will develop now that Arena Trap is banned?
I think fat will die out somewhat and become more balance oriented. Toxapex and Clefable appreciate not being trapped by Duggie, but the cores they worked well on took a hard hit from losing the mon that allowed for them to keep their defenses intact. Contrarily, though, Hippowdon is on the rise, and I highly expect it'll become even better now that Terrakion and Zeraora are going to become more prevalent.
As stated above, I think Screens will become more prevalent as well as a way to combat and capitalize on the fact that Duggie can't trap setting up Zeraora/Terrakion, allowing for more aggressive HO playstyles to maybe flourish on the side.
6. Is there anything that may become too problematic for OU now that Arena Trap is banned?
This is really hard to say, but I'm looking toward Kyurem and Zeraora if anything. I want to make clear that
I think we definitely need time before we suspect anything else, but these two are the ones that stand out to me the most right now.
I believe Kyurem's potential is a bit overhyped due to the prevalence of SpDef Clefable, the rise of SpDef Corviknight, and the new prevalence of common offensive checks like Terrakion and Zeraora. But, I think this thing is still extremely dangerous and might be worth suspecting down the line depending on how the meta shapes up.
Zeraora I feel is a bit more cause of concern, and it's because of one move: Grass Knot. Unlike Kyurem, it doesn't really have a consistent answer, as things like Hippowdon and Seismitoad are hard checked by Grass Knot, and it's not very hard to chip down Hippowdon to get it in range of the KO. Additionally, it's much more offensively versatile than Kyurem, and if you get the set wrong, it can pretty easily set up with Bulk Up and dismantle your team. It has a pretty similar problem to Gyarados in UU where if you predict the set wrong, you can and will be punished hard (but not to the same degree, I feel). It's true that Rotom-H is a pretty good answer, but Rotom can get pretty effectively chipped down, and since it can't recover reliably, it will fold to Bulk Up sets. I mentioned Screens earlier as well, and Zeraora will be a pretty scary example of what can come of it if not prepared for.