Hello,
1) I checked your site and don’t see the problem with the logo https://prnt.sc/BAT6xXcG_EOe
Besides, I don’t see the problem with the logo even on the video that you provided.
2) I checked the site and the mobile menu works ok https://recordit.co/9Zm5H3bvJY Without any problem. Besides real content is completely different than on your video.
3) If you add the static block content for the More toggle 02 and you want to show it then don’t forget to add the More toggle 02 item to mobile content. Once I added I don’t see any issues with it’s appearance https://gyazo.com/dd0df8d9c164286a962a29b96ce96d60
Regards