Because Rasengan hit Preta Path and then got absorbed. Same situation with V2 Bee. Preta didn't create a barrier around his body which nullified the properties of the chakra from the get-go like he did against FRS. He literally touched the Rasengan and massive impact against his hands/face occurred before he started absorbing/negating the Rasengan. Rasengan was negated after the impact just like V2 was, yet in both situations said 'impact' did absolutely no harm. And no, the power of V2 Lariat is mostly Bee's speed/physical strength and the chakra around him being a mere bonus given its hardness. Base Bee>v1 Ay Lariat wise, so surely the v2 speed/power enhancement is not necessary to inflict damage (he still did have it though given it added to his momentum/initial impact).
But Rasengan did nothing to Preta Path. Didn't damage it nor did it push it back in any way, shape or form despite getting "hit". The same can't be said for Lariat as we can clearly see in the scan where he gets hit and he starts to get thrown back. The two scenarios are not the same and thus are not comparable. If they were the same Nagato wouldn't have budged and inch and then he would've sucked up B's chakra and blown him away.
And no, Base B's lariat isn't stronger than V1 Ay's lariat. B is physically stronger than Ay so if they run at the same speed and clash with each other obviously B will win. Ay didn't use Shunshin, he simply ran at Killer B. Ay uses the armor to boost his speed thus increasing the force he puts out using his lariat. Manga has already stated to use Double Lariat both Lariats have to be equal in power, and V1 Ay and V1 B matched each other and decapitated the Zetsu Kisame. Meaning full power V1 Ay Lariat=Full Power V1 B Lariat.
Is it necessary to inflict damage in general? No, but against someone as durable as Nagato? Yes, it is as there is a large gap between V2 Lariat, V1 Lariat, and Base Lariat. Each state increases speed, physical power and damage potential due to the nature of the chakra wrapped around the user.
It's the same exact thing since neither is using CES. Ay's Lariat is amplified via speed/power boost/body becomes so hard it deflects sword, identical to Bee. They're both shrouds, only difference is Ay's is transparent (otherwise it wouldn't increase durability but it canonically does).
But taking away Ay's shroud does nothing because the majority of his power isn't from his shroud. It's from Onoki's jutsu and the momentum generated by his speed which can't be changed after the fact. The same doesn't apply to B which is why your examples don't connect and don't hold any weight.
And I agree on that, but he'd need prior knowledge of this because after the first failure it's all over via soul rip.
No, it's not, because he'd still be sent flying regardless of negating the damage as B's lariat made him move regardless of the fact it didn't do damage. He has the Rinnegan, and they know that Preta Path is an ability due to their fight against Madara so it doesn't even matter regardless.