It is not normal for your turtle's shell to be soft. I don't think you have a proper basking spot. The rock that your turtle can get dry on should have a heat light on it for 10-12 hours a day. It should be about 90 degrees on the rock and the water should be in the low 70's. You also need a UVB light to help the shell form properly. I think you need to make these changes immediately, I don't know how long it will take for the shell to harden. You should also get some cuttle bone. It is available in the bird section of the pet store, just scrape off the hard backing and throw a piece in the water. He might not know what to do with it at first. Eventually, he will eat it and the calcium it provides will help with the shell.
Hopefully one of our more experienced keepers will chime in if there are any other remedies for the soft shell. You need to get a good basking spot NOW, even healthy turtles need that.
Good luck!