No no no no no........ She is definatly a Skywalker. But not Leia's and Han's. She is Luke's. No doubt. They all had a familial bond with her but the grief you see in Han's face is his knowledge that his son Ben was the cause of her abandonment. Yes she lost her childhood and it was Ben's fault. Though she was too young to remember.
I think it was Han that maybe had to abandon her on Jakku. Or at least he suspected that she was there. He sounds pissed at himself that the Falcon was there and he missed it.
And Leia thought the daughter of Luke was dead until she sensed Rey through the Force and knew only his daughter could bring him back. All his self exile is now in vain.
And the look on Luke's face when she shows up. Its pain. He spent all this time away trying to protect her and now its in vain because she will follow in his footsteps anyway.
Plus she is mechanical. Anakin Trait.
She is an awesome pilot. Anakin Trait.
She is a natural leader. Skywalker Trait.
She is Force sensitive. Skywalker Trait.

Her and Kylo defiantly fight like siblings but there is no recognition in either of them. So that ones a tossup.

There is one thing that has been bugging me. Maybe you can help me out. At the end of the sequence in the basement of Maz's cantina. When she falls back out into the hall after finding the lightsaber. There is a whisper at the end of the audio. I can't make it out. Tried looping it and still can't hear it. Too many years working on loud ass harleys. But someone or something whispers something. And its not Maz or Rey.

Excellent post. Dammit I can't wait till December 15th. My son is 9 and its awesome getting to relive the Star Wars experience with him. He loved The Force Awakens and Rogue One. I loved both of them and getting to watch them with him in the theater. Priceless.

"I am one with the Force, the Force is with me."

RIP Scruffy Looking Nerf Herder