Are water and vertical cracks normal for full height crawl space?
I think the things you mentioned are solvable, though cannot venture a guess as to the cost.
First thing is to identify the source of the water in the crawlspace.  The ground around the house has a good slope towards the back, so it should be relatively easy to direct any surface water away from the foundation - much easier than if you had a totally flat lot.
The (I guess) minor vertical cracks in the basement wall are easily fixed with an epoxy compound that is injected into the cracks, assuming the cracks are not growing. I had something similar in my previous house, noticed right after we moved in, and the epoxy-injection fix I mentioned held up for the 21 years we were in the house.