Invincible force? Kyuubi Naruto stuck his tails into the ground and withstood Shinra Tensei, head on. Not so sure that "invincible" is the correct word.
I think you mean "Yahiko" not "Yugito"? But, I don't think it was so much because of Yahiko's death, which is why one of Nagato's paths resembled him, but more so the constant wars in which Nagato was tired of. Someone (Tobi) offered him a way to cease all of it, so he just went with it...
OR... Because Tobi shares the same Mangekyou ninjutsu, he went into the other dimension himself and got Deidara's arm????
No, Gai is fodder who Kishimoto tries to remain relevant for this purpose (fight with Tobi) with an ultra-super-duper Naruto power up (the gates) which ironically doesn't...