Is it normal for collaborator to rerun experiments himself?
I don't find that behavior strange at all. If I want to understand problems with algorithms (I don't do experiments with anything other than algorithms) I need to run them by myself and sometimes even implement the method from scratch. It's not that I do not trust other people's code, but if I want to understand all the mechanisms well, it's much easier to get a grip on it when I've done it myself.
The other way round, I do not have any objections if a coauthor of mine re-implements a method I already provided just to see how it works. On the contrary: Usually I benefit from this in one way or another, e.g. by learning new tricks or getting rid of bad programming style…
When I was a graduate student, I was working together with another student who implemented a rather complicated numerical simulation. To understand it better, and to do some additional experiments with this model, I decided to re-implement it myself. I was not able to get the same results as the other student. After a thorough review of my code, I found a minor mistake, and corrected it, but I still wasn't able to reproduce the other student's results.
In the end it turned out that the other student also had multiple mistakes. We fixed them, and finally everything matched up.
We had two independent implementations of the model we were studying, and finally they were giving the same result. Only at this point was I fully confident that our results were correct.
Double-checking makes a lot of sense. Mistakes happen, quite frequently. I would never trust a single result, either mine or someone else's, nearly as much as an independently verified experiment.
I have also worked in an environment where it was frowned upon to double check a coworker's work, claiming that "it is a waste of time". In reality, people were afraid that their work would be overtaken or stolen, and they were withholding data in order to prevent others from checking their result. In the end, it turned out that some results I was relying on were plainly wrong, which resulted in even more waste of time in the end. My advice is to try to avoid creating a toxic environment full of jealousy, like the one I experienced. Double checking is always a good thing.
I don't see any problem with your collaborators wanting to be sure of things. I also don't work in the experimental sciences but any time one of my collaborators emails me a page of mathematics, the first thing I do is check it line by line to make sure it's really true, and the second thing I do is try to improve it.
It sounds like there's a bit of a communication problem between you and your collaborator. Also, if your collaborator is an established researcher, they might be being a little impatient with you and forgetting that, as a brand new PhD student, it's going to take you a little longer to get things sorted out.
Talk to your advisor, as always. If you're upset by what your collaborator has done, tell your advisor about it. They'll either explain that things are OK, or agree with you and talk to your collaborator about it.