Would Harey (or an other Visitor) 1. regenerate her hair if cut? 2. Grow her hair or fingernails? I assume the answer to question 2 is no, because it is stated in the novel, that she will not age, but even that is only speculation.
Harey is an image constructed by Solaris from an image Kelvin's deep memories.
I don't think she would have thought to trim her nails or cut her hair. The novel does not give evidence that they grew naturally over the several weeks on board the station.
Other strange things happen that she brushes off or ignores (at first). Example: Kelvin has to cut her dress off when she wants to change clothing. The dress does not regenerate and the novel does not mention it disappearing either.
When she consents to a blood test, her skin and blood react exactly like normal human skin and blood. The changes found by Kelvin were at (or below) the molecular level.
I think that if it had occurred to her to cut her hair, she would have been able to just like a normal human. Her hair wouldn't have gone back unless something happened to reset the original "Image".
Examples: when Kelvin "divorced" her the first time, or when she crashed through the steel door, or when she tried to commit suicide. In the first case she was completely reset to the original image, in the second two her wounds very quickly returned to a whole state.
Edit: In the novel, the scientists discuss some of the limitations after the blood test. Basically Harey's body contains enough energy to maintain and regenerate it almost indefinitely.