How to get permission from Google to use Google Scholar Data, if needed?
Google Scholar, as you said, does not provide API, nor a complete documentation.
In the comment Davidmh cites this question, and I think that settles everything:


Google Scholar robot.txt disallows bots
Google service Terms of Service says


  Don’t misuse our Services. For example, don’t interfere with our Services or try to access them using a method other than the interface and the instructions that we provide.
  
  So, in the end, you don't have permission for a script that fetches multiple pages at a time.   


Following this Quora question, I found scholar.py, that is not an answer to your question but could be of use (I have not tried it). 

Furthermore, I also asked the developer of the H-Index GS Calculator, to get another opinion, but I'm sure the "one-click" nature of the plugin complies with the ToS. A bot does not. Maybe you can change your system in this direction.

UPDATE: the developer says the in the past he wrote the GS team the same questions, and they replied 


  
  you can do stuff, respecting the ToS (so, no bot)
  they will not provide an API, for legal constraints with affiliated digital libraries (ex. Scopus, WoS, etc.).
  


Also, his calculator has a throttler that reduces the number of queries per minute, to mitigate the issue. There are few simple techniques to "cheat", but, we are at the boundaries of the ToS :-).