Basically just a tl;dr ooc thing for my own reference. Urataros' thoughts, relationships, personality based on his current timeline and events in the City.
Urataros is taken from early episode 48, before he spots the Mole Imagins planting a bomb on the Den-Liner. When he opens the door to the main control room he instead finds himself inside a random bar in the City.
The City:
The first thing Urataros notices is that he's in his physical form, which is kind of weird because as far as he knows only Kintaros had been able to remain in his physical form outside the Den-Liner. He concludes that this must also be an effect of Ryoutarou's wish continue fighting with everyone and that he's somehow subconsciously granting it. He also would note that he's not disappearing anymore. Buuut he's still confused so he explores the Network a bit, which is where he finds Ryoutarou's entry.
So yes, Urataros would have looked over Ryoutarou's entry, thus getting access to the City Guide and finding out about Tsurugi and other Riders from multiple worlds, and Yuuto being here before (though it's unclear whether Deneb has been present, too, since Yuuto and the "other" Ryoutarou didn't reveal much to Tsurugi). He knows that he's in the year 2010 and that they're in another sort of "universe", which doesn't seem logical at all, but the guides sort of support it. Another thing he notes is that people arrive from different timelines, so there's a possibility that Ryoutarou could have come from sometime in the past or the future, as well.
Despite knowing that he's supposed to be fighting alongside Ryoutarou and the other Imagins back in their world, and despite he himself telling everyone else that their future isn't with Ryoutarou's, he can't help but feel a bit relieved to be in the City. He isn't disappearing, for one (probably because this world isn't connected to any time and thus no type of "time" i.e.: Imagin's future, present, past, in their world influences them in this place-it also means that there is no future that's disappearing, though it's strange that he's still here despite the absence of their time), and though he's supposed to get over it he can't help but still be a little bit selfish. He also knows he is, but what can he do about it? He had thought it was okay that his and Ryoutarou's future aren't the same, and he even DID disappear once. But watching Kintaros leave the Den-Liner is probably the wake-up call he got: In reality he's still very much concerned with his existence and he doesn't want to disappear. I think though he acts cool about it, he's genuinely afraid of fading away.
At the same, though, time he wants to prevent the Imagins from connecting their future time to the present time, because he genuinely cares about protecting Ryoutarou and everyone in it. He's aware that it's contradictory, but he's just not ready to choose one over the other just yet. Deep inside, he knows the right decision to make; still, it would still take something big for him to realize it.
He's heard about the curses and deities and it kind of bothers him a bit that Ryoutarou could be hurt from those curses, but he's resolved to try his best to protect Ryoutarou from it. Once he gets to talk to Ryoutarou he will be checking if Ryoutarou's from another point in time. He would probably lie and say that he's from the same time line as Ryoutarou once he learns that Ryoutarou's from an earlier one, because he wouldn't want Ryoutarou to be burdened with the thought that Kintaros has been left behind and has possibly disappeared while fighting in the past. There's also that bit with the past!Airi appearing in the Den-Liner. Tl;dr he'll keep a lot of things to himself.
EXCEPT LOL NO. Hi Ura, have your first curse! Ura's first curse basically has him acting like the terrible, selfish manslut he is in the early episodes so LOL GJ URA. Once the curse ends he'll actually feel pretty bad about it (that he took advantage of Ryoutarou, not because he hit on those all those pretty girls). He'll mention to Ryoutarou that Ryoutarou really didn't leave him and the Taroses all sad and depressed and waiting forever (l-lol) and probably say that curses are inconvenient, which he hopes Ryoutarou would understand as his somewhat-trying-to-say-sorry-maybe thing. Because the thing is, Ura doesn't apologize. And normally he also wouldn't feel really guilty about anything but hey, this time Ryoutarou didn't even call for him before he possessed the kid. He knows it's not his fault, but it still seems to be the right thing to do-maybe Ryoutarou's rubbing off on him. He also thinks that curses are both a good thing (like getting to talk to/flirt with Ivy) and a bad thing (like letting him do things he doesn't want to). As for the deities, he's not really sure of what to think of them just yet. They seem like asshats from what he's read in the guides, but at the same time the guide says that there are other creatures stronger than the deities. He doesn't really know whether the deities are really just jackasses or whether there's something much bigger going on.
Regarding revealing himself:
Like in canon, Urataros will not reveal himself and will talk through Ryoutarou. He might be more willing to introduce himself if something in the future happens (like idk the other Imagins ruining everything and getting found out). He will never reveal the complete truth about himself, though, unless it will benefit him and/or Ryoutarou. First off, it would be kind of troublesome because he kind of introduced himself as Ryoutarou to everyone. But the much bigger and more important problem is that not everyone in their world knows about the Imagins possessing Ryoutarou. He's just thinking of what would happen if the people Ryoutarou knows but who doesn't know he's being possessed by Imagins would appear; essentially, it would be a problem.
Regarding the absence of the other Imagins:
It's actually been rather quiet without the other Imagins present, and Urataros actually misses them-somehow he's grown used to the noise. He would want them to be here with him and Ryoutarou, though he would never, ever admit it out loud. Since he's the only Taros in the City he feels like he has some kind of responsibility to look out for Ryoutarou while the others are gone, so he's going to step his game up a bit and be a bit more protective (especially now that Momo isn't around to do that). This kind of protectiveness becomes really obvious when he took it to himself to care for Ryoutarou's wounds when bugs had descended on Ryoutarou during the Plagues curse, and again when he took some lamb's blood (through flirting with a butcher girl, of course) and painting blood over their door. He's heard of only the firstborns getting killed off by the Angel of Death, of course, BUT EVERYONE KNOWS RYOUTAROU'S LUCK IS TERRIBLE AND WHAT IF THE ANGEL OF DEATH MISSES AND HACKS RYOUTAROU BY MISTAKE. OR WHAT IF RYOUTAROU TRIPS AND FALLS ON THE ANGEL OF DEATH'S SCYTHE. Anyway, Ura just won't take any chances, so yeah.
Relationships:
Ryoutarou: Initially just there so Ura could have a body to possess when hitting on girls, Ura's grown really attached to him. I think he's really impressed with Ryoutarou's determination and selflessness and just him caring for everyone, even Imagins like Ura and the other Taros. Urataros would totally go along with whatever Ryoutarou wants, like, you know, transforming into Den-O's Rod Form and saving people from curses and stuff like that. It seems like Ryoutarou just has a lot of belief in Ura, and though maybe Ura initially just thinks nothing of it, he does eventually begin to appreciate that unwavering trust and faith that he actually begins to become really fond of Ryoutarou. It seems that Ryoutarou would do anything to protect Ura (even way back when Ryoutarou agreed to let Ura stay on the Den-Liner), so Ura's just doing the same for Ryoutarou, even when it means disappearing and even if he's scared of it. Because, you know, they be bros, man.
*I think Ura isn't the type to get close to people immediately. Sure, he likes girls, and sure he'll flirt with them, but it stays at that: flirting. It takes a lot before Ura can get attached to someone, but when he does, oh man will he give up a lot for them. Though at this point he's still unaware that he could even give up everything for the people and the time that's important to him, if such an event happens where he's forced to decide, he will definitely fight to the death for those he cares about.
People Ryoutarou's talked to:
People that Urataros should be familiar with because Ryoutarou knows them too: Tsurugi Kamishiro, Kate Todd (who he will hit on), Ruca Milda, Ivy Tamwood (who he will also hit on), and Setsuna never said his name but Urataros probably researched it lol so Setsuna F. Seiei (though he notes not to know his name until someone else tells him)