1) Use responsive options of the heading element http://prntscr.com/s1dx5z
2) Provide us with FTP access to your site to fix this issue.
3) Unfortunately, there is no such option in our theme. It’s possible only by additional PHP customization that is not included in our basic support. (XStore theme allows to place wishlist to header because it comes with header builder.)
4) There is no such option by default. Search icon in the Royal theme has only such design. If you want to change it you can do this only by additional customization. (XStore theme allows to choose between 2 designs of the search http://prntscr.com/s1elpd and use different for the mobile and desktop versions)
5) I have changed the colors by minor CSS customization. Check now.
6) Fixed. Check now.
7) XStore includes more options to customize header, footer, products to suit your needs because include the advanced module based on customizer that allows checking the changes in real-time. Watch XStore video tutorials to get more information about it https://www.youtube.com/playlist?list=PLMqMSqDgPNmCCyem_z9l2ZJ1owQUaFCE3
Truly saying looking at things you want to change I would suggest you to try XStore even for the current project. XStore also uses the WPBakery page builder, so you should no face a lot of issues after migration. We could exchange Royal to XStore if you want.
