Hello,
1) Compare code you provided in private content area and our code http://prntscr.com/s4r6mc Don’t you see the missing shortcode attributes? Icons were one per line because you added shortcode to text area instead of the Raw HTML if you want to use HTML code http://prntscr.com/s4r814
Anyway, I have rebuilt the page using WPBakery elements and put custom classes for the section and rows https://gyazo.com/4617299626cf2b19a566ad728a639129
2) Edit the row and upload the bg image for this row https://gyazo.com/deed58430f6e4f7bdc0f6f7febf02339
3) Yes, sure, why not? Just drag and drop the carousel element to previous row https://gyazo.com/9976533ad3e130fcce8b87cea380bcf2 Also, you can manage any row bg color using the Design tab in the Row Settings.
4) Create mega menu using Static Blocks. Watch the video tutorial https://youtu.be/f07MBdnFPfk
Regards