Hello,
2) Google fonts are integrated in right way. Provide me temporary admin panel and FTP access to check the settings.
4) It styles. We have 3 types of buttons on our site – light (for example http://prntscr.com/hdcwhy), dark (for example http://prntscr.com/hdcwxi), active (for example http://prntscr.com/hdcx3r) and you can style them all via theme options http://prntscr.com/hdcxly
5) We’ll add options for the fixed header and border in next theme update.
Regards