Queries regading Überweisungsschein

I have public health insurance and recently booked an appointment with a doctor through the DoctoLib app. I went to the clinic, filled out a form, and then had a checkup where the doctor did a general exam, gave me a flu shot, and asked me to come back in a week for blood test results. When I went back, she said everything looked good, and I mentioned another issue I wanted checked. She then gave me an Überweisungsschein (transfer slip) for a specialist.

Here are my questions:

1. Does this doctor now count as my Hausarzt since they have my details on file?
2. Can I use this Überweisungsschein at any clinic where the specialist is available, or is it tied to a specific clinic?
3. How long is the Überweisungsschein valid? Can I use it after a few months if the issue isn’t urgent?
4. I noticed I can book specialists directly on the DoctoLib app. In that case, does the Überweisungsschein still matter?
5. If I see a specialist through DoctoLib without a transfer slip, do I need to let my Hausarzt know about the results?