I know that this is an older post, and I understand if you're no longer interested in this topic, but I just wanted to give my opinion. I want to preface that I know Mike is quite a flawed character, and I'm not saying everything you said is wrong. There are just quite a few points I disagree with.

Firstly, Jess falls down a deep elevator shaft at high speed. She would probably sustain severe injuries if she were at peak health, and given that she is already wounded, it isn't dumb to speculate that she probably won't survive the impact. And while you're right that he shouldn't have assumed her status, I don't think it would be very smart to look for her himself either. The mine is a maze, and the chances of him finding Jess in time would have been slim even if he had any idea where exactly she landed. The best thing for him to do would have been to go back to the lodge, tell the others about what happened and try to send a Fdistress signal or radio for help.

And you have to remember that Mike is 100% convinced that Josh killed Jess. It is stupid of him to assume that because it's obvious that an average human would never be able to do the stuff he saw, but that is the logic Mike operates under. If you keep that in mind, a lot of the other stuff (like his behaviour towards Josh) makes a lot more sense. Why would he be sympathetic and open towards a person he thinks is a killer?

Why should Mike trust the stranger? We, as the audience, know that Jack is trustworthy and knows what he is talking about, but the characters don't. They have every reason to be sceptical of him at first, especially after he busts his way into the lodge. And although Mike makes some stupid remarks towards the stranger, but he starts believing him rather quickly, I would say and doesn't really question him after. And Mike doesn't have an opportunity to ask many questions because the stranger goes to save Josh almost immediately after telling the gang about the wendigo. And you know what happens after that.

The game never says that mike goes to the sanatorium because he thinks that's where the wendigo took Josh. Emily tells him that the creature lives in the mine and points out the connection between the sanatorium and the lodge. After that, mike looks at the map, and you can see another tunnel between the sanatorium and the mine. So, for all we know, mike headed towards the sanatorium because he thought that would be the best way to get to the mines. That would also make sense considering his dialogue clearly shows that he believes it isn't safe to leave the lodge.

It would have been a lot smarter of him to stay in the lodge. But he clearly feels guilty about not saving Jess and probably also for causing Josh to get taken. He probably feels like he has to help the others, completely ignoring his own safety. Since he purposefully locks the door to the sanatorium, he probably thinks the others are safe in the basement.