That's a very clear requirement, with supportive link. I could help you in further refine the code to match your requirement.
At the end, you shall get a new menu in the spreadsheet, and when you click it, the required sheet shall be converted to PDF, and send to the respective email id.
Something about myself, I have enough experience in Google script, which is required for this project my previous projects are almost in Google scripts.
Hope we could start