The use of Grand Theft Me leads to some Fridge Logic about the choice of victim. The criteria that the vessel be a healthy non-Duelist whose possession would hurt Yugi applies to both Anzu and Honda. Sure, she's the Love Interest, but wouldn't a boy be a more preferable vessel? The Abridged Series would have a field day with all of the implications...
Though in volume four, when the RA project nears completion, it appears that Anzu's body is merely being used as fuel to recreate Pegasus's body with The Wicked Avatar. Not that it matters too much in the end...
There was originally a rule that fusion monsters couldn't attack on the turn they are summoned. Kaiba probably had to end his turn after fusion summoning Ultimate because of that, giving Yako another turn.
Which begs the question... Why bother fusing them? Why not just take the one Blue-Eyes White Dragon that could attack at that point and end the game with it? Anything he risks with that, he still risks with the Ultimate.
Also... While the fusion attack rule was present in the original series, the Special Rules section in the same volume, by the writer, Akira Ito, presents no such rule. Which... Really just makes it all the more baffling.
Well, Yugi also had to wait one turn before attacking with his fusion monster when he dueled Yako/Gekkou in the second volume, so it looks like the rule was in effect. Also, I thought Kaiba summoned the Ultimate Dragon just to humiliate Yako, which isn't really unusual.
To answer the main question, Kaiba had a Field Card Alpha-Wave Emission which prevents all monsters face up from attacking unless they were equipped with Vaccination to negate that Field Effect. Only one Blue-Eyes White Dragon was equipped at the time with the Vaccination card, so the other two could not attack. You are correct in that nothing else was stopping Kaiba's Ultimate Dragon from winning him the game then, but that unfortunately must be chalked-up to Plot Armor for Yako.
That and Seto isn't new to holding the Idiot Ball. In the Duelist Kingdom saga he could have defeated Yami by using a Negate Attack to earn that one turn he needed to win (he had one in the field), but he opted for treathening to jump from the tower instead...
In the climactic final duel between Yugi and Yako, Yako manages to summon the Wicked Avatar, which always has one more attack power than the other strongest monster on the field. Yugi works his way around this by summoning Obelisk the Tormentor and activating one of his special abilities - sacrificing two other monsters to make Obelisk's power infinite. Had the monsters drawn there, no headscratcher would exist, but Yako states that the Wicked Avatar is in a different league to Obelisk and will still win, until Yugi brings out a spell card which adds 1000 attack to Obelisk. So... they both have infinite power, but the Wicked Avatar's infinite power is greater than Obelisk's infinite power, so Yugi adds 1000 power to Obelisk's infinite power so that the infinities are now equal. What?
It's related to some particular rules regarding the God Cards, that are explained more clearly in the manga- Ra is a more powerful god than Slifer/Osiris and Obelisk, so their effects don't normally work on Ra. The Wicked Avatar is sort of the evil counterpart to Ra, so it has a similarly higher status, which in this case results in it initially winning when their attack points are both infinity. Yugi's equip spell "promotes" Obelisk one step up the divine hierarchy, meaning it's now equal standing to the Avatar.