Why does Gorou, upon assuming Zolda's identity, stick to using ranged attacks, despite being a good hand-to-hand fighter? Because he didn't want to give away the deception to Asakura.
Ren/Knight, despite having little or no qualms about fully participating in the Rider War, can't bring himself to kill another Rider, and the one whom he did, Odin, never really died in the sense of the Odin persona remaining alive. It makes more sense when his status as a Batman Expy is remembered.
It can also explain why there are multiples of him running around.
Asakura's death scene makes a lot more sense when you realize he's obsessed with finishing what he started. Look at how he manipulated Reiko into tracking down and reuniting him with his brother, all for the sake of getting another shot at him. That was years ago, when they were kids, but he never forgot and was probably thinking about it all this time. Now he spent the whole series trying to kill Kitaoka, and failing. The weaselly lawyer always got away. After what happened with his brother, he probably decided he would never let someone he was trying to kill escape. When he again failed to kill him, it finally drove him insane... well, more insane.
If you watched Kamen Rider Agito, you'll know why the evil Agito Burning Form, existing simultaneously with regular Agito in the Ryuki vs Agito short, isn't that farfetched an idea.note The premise of Agito states that certain humans can evolve past humanity and into an Agito, and it's happened to several characters already (Shoichi, Dr Kino, Shoichi's sister in the past, and Ryo/Gills could also count)
It also relates to how Shinji had a mirror copy who was downright evil.
Ren's later horror for when seemingly killed Odin and unwillingness to kill Jun seems to run contrary to how he didn't bat an eye to when Sudo was killed by Volcancer after Ren broke his deck, but when one thinks about it, Ren didn't deliver the killing blow on him, Volcancer did, so to avoid admitting to himself that he was responsible for Sudo's death, he simply thought of Volcancer as the real killer.
Compared to other Rider series, Ryuki Riders seem pretty fragile. In most series, getting hit with another Rider's Finishing Move might knock you out of transformation and rough you up, but won't kill you unless it's at the end of a major battle or something. But here, getting nailed directly with a finisher is much more often fatal, not to mention how easy it is to break the Advent Decks. This makes sense when you remember with the exception of Odin, all the Riders are 'supposed' to die. The Riders in this verse are intentionally more fragile than the Riders of other series for obvious reasons. To add support to this, in Decade the alternate universe Ryuki Riders, which lifts the fatality of said obvious reason, are typically just as hard to kill as most Riders.
So without Verde, Femme, and Ryuga, who constitutes as the three riders to fill out the Thirteen Riders in the war? The two other Odins and the extra Zolda. There Ain't No Rule saying that all the riders have to be unique.
Given that it's specified that thirteen Rider Decks exist, it might just be that in the TV timeline, the recipients of those three decks just happened to be eliminated off-screen. They may have even been some of the people shown in the OP with their eyes scribbled out.
If you notice, a Final Vent is really a Combination Attack between the Rider and his monster, or some form of team work. The only exception is Abyss.
Dragon Rider Kick: Drag Redder/Blacker gives Ryuki/Ryuga the fire they need for their Rider Kick.
Hishozan: Darkwing wraps itself around Knight to act as a giant drill.
Scissors Attack: Scissors jumps off Volcancer's claws.
End of the World: Zolda simply pulls the trigger to unload all Magnugiga's ammo.
Hide Venom: Raia rides on Evildiver.
Heavy Pressure: Gai rides on Metalgelas
Veno Crash: Pretty much like the Dragon Rider Kick, but with a snake instead.
Crystal Break: Destwilder brings the victim to Tiger for the final blow.
Drive Divider: All of the monsters that Imperer has in his control come and attack while he lands the final blow.
Misty Slash: Blancwing blows people towards Femme who slashes them.
Death Punish: Biogreeza grabs both Verde and his victim with his tongue and then flips them around.
Eternal Chaos: Odin and Gold Phoenix essentially go into a Suicide Attack.
Knight has a bit of a rivalry with Ryuki, to the point where he nearly kills him. In short, it's the knight trying to slay the dragon.
In future crossovers, Ryuki and the others appear, rider belt and all. At first, given the concept of alternate universes as presented by Kamen Rider Decade, this might be a good explanation of how they have their decks even when the Reset Button Ending states that they no longer have those, but you then think a bit carefully, and you realize that somewhere in an alternate world, the war never ended. It's more bone-chilling when you consider the alternate endings, where a good chunk of them are Bolivian Army Endings, and one of them ended with the war resetting, just that now Shinji has Ren's deck. Though thanks to Ryuki's Hyper Battle Video and Decade's take on Ryuki, where the riders are either heroes of justice or lawyers respectively, it could be possible that the Ryuki Riders came from those universes.
Asakura is consistently shown to be one of the deadliest (if not the deadliest) fighters in the Rider War; he only dies in the final timeline because he chose to. His stated wish is for the Rider War to go on forever. It's entirely possible that he's won the war before, maybe even multiple times, because when he wins he just wishes for the whole thing to restart. Hell, think about it too much, and you might think he's the reason Time Vent even exists in the first place.