Both the usages are correct but
what kind of hobbies does she have
is more in use.
What kind of hobbies has she?
What kind of hobbies has she (got)?
is mainly considered to be BrE.
Both sentences can be correct:
This is one of the things which is really important to her.
This is one thing. It is really important to her.
This is one of the things which are really important to her.
Out of all of the things that are really important to her, this is one.
So, either one thing is important, or the things are important. In the singular meaning, the other things might or might not be really important to her.
Another difference is that
This is one of the things which are really important to her.
needs no previous referent because "things" is general enough to be understood generically, whereas
This is one of the things which is really important to her.
needs a referent for "things" because "one" makes it specific:
There are many interesting things in her life, some important, some not. This is one of the things which is really important to her.
Adding a comma makes the meaning clearer:
This is one of the things, which is really important to her.
Best Answer
The answer is that neither is correct.
If you use this kind you need to retain the singular of story in the same way that you would speak of this kind of house.
Alternatively, you can say these kinds of stories.
This construction takes the plural because the subject is plural. It is both this story and these kinds of stories:
A similar example, that makes things clearer, would be:
You will find helpful examples and explanations of Subject-Verb Agreement at a number of sites such as:
https://www.grammarbook.com/grammar/subjectVerbAgree.asp https://academicguides.waldenu.edu/writingcenter/grammar/subjectverbagreement