I'm not sure what's your role in the project, I'm supposing you are the PO. In that case, use additional documentation if it makes sense. Consider a user story as a reminder for the team to have a conversation with the PO about it.
If you think the user case diagram will clarify the functionality you are asking for, the it's ok. In fact, place it on the wall beside the scrumboard and burndown chart.
In my experience it is sufficient to specify for each story a "how to test" scenario. For example, suppose I have a story for Stackoverflow:
"As a user I can post a new question"
The "how to test" scenario could be:
"Click on a 'Ask Question' button, a form is displayed with a textarea for the question text and a textfield for tags. After the user enters both -they are mandatory- the user is redirected to the question list. The user can see the question title in the list, along with the tags"
So maybe a use case diagram is not really needed. I would recommend to try the "how to test" and see how it goes. It is very useful for the team because they know what you are expecting from the story, from a functional point of view. And you won't be doing documentation for every story.
If you don't like it, the go with the use case diagram, but it is a good idea to give the team something more than the story description.
Now, about the technical stories you mention. What are they? Why is a technical requirement mixed with the functional requirements? Maybe it IS a real requirement for the project, but usually it is not, and can be rewritten as a functional story. Unless your product is something like a framework or library.
For example, the technical story "create indices for the 'get questions' query" could be rewritten as "speed up the questions list page".