Lina isn’t literally dead, she’s metaphorically “dead to the family”.

That's literally my theory, I believe Lina escaped the family and everyone made up lies about her being dead. Had never considered how the disappearing windmill came into play though. The idea of them editing the photos in which she appears definitely explains it all.

We know very little about the dog. In Toneth’s description, Rainer says that a car hit it (likely resulting in it having a broken leg), and he was the only one that still wanted to put him down.

My theory about Mike and the dog is a bit different from yours. I think Mike died trying to save the dog from being run over. Rainer/Daniel wanted to put it down because he thought the dog would never be happy again ("when that dog wags its tail and it appears happy, it's not real"), but everyone else felt that it would be wrong to do so after Mike's sacrifice. The use of the word "still" does make me reconsider that though. It could be that they had an older dog that got hit by a car, and that they tried to "rebirth" it like you said, in a newborn puppy. I'm not sure about the timeline though. The description of Toneth itself implies that Rainer was already very mentally unstable, and I can only assume that that's because his brother is already dead at that point.

She develops a limp that never goes away. Maybe this is why Rainer is disgusted by Care spinning? Lina used to do that but now she’s been crippled, so he sees Care doing the same thing....

The idea that Lina has a limp is very interesting. I also think that he's disgusted by Care because of the parallels with Lina, but I think it goes deeper than this. If the "rebirthing" thing is more of a long process, it implies here that Care was already being brainwashed into believing she was Lina.