But is it possible to simply move the existing menu and place it underneath the logo ?
You can try achieving this by using the child theme solution posted in the following topic.
https://colorlibsupport.com/t/logo-above-menu-bar-social-icons-on-top/
I also have a question about the flexsider (I want it to show only five slides), but I don’t know if I have to create another thread for this question?
Yes please create a new thread for it.