Hello,
Thank you very much for choosing our theme and contacting our support.
1/ Please navigate to Theme Settings > Header > have you enabled Header Builder if so: Please navigate to Woodmart > Head builder http://prntscr.com/iyd2pe
Choose the proper header type (your current) http://prntscr.com/iyd333
Modify elements as per your needs: http://prntscr.com/iyd3h3
Take into consideration that there is also the mobile view of your header http://prntscr.com/iyd3v3 check all the elements there.
2/ Not all the svg format are supported. Upload you svg file into note++ or equal add fixed width and height and replace to media, if it does not work, choose another svg format or use png.
3/ Categories, choose the proper design in Category element http://prntscr.com/jn5cji
Best Regards