Awesome site! I can see your problems.
Here are the solutions
But before we start, never have body as a parent to a slider. It confuses the slider arrows.
Okay lets begin
IMPORTANT! Do all these changes in desktop view, so they can cascade down, if not stated otherwise.
Your first and third problem can be fixed by doing these steps.
Inside of header section. change Margin top to 0. If you still want the same effect, give padding top 60 px instead. (Don't use margin that much on section elements. It shows the body behind it.)
Go into tablet view now. Click on your nav menu icon and open the menu. Go to your Nav Bar class and change the Position to Absolute top. Now go to your Nav Menu class and also set its Position to Relative. ( Not the same design, but I couldn't find any solution to fix it ), also change background color to white
If these steps aren't making a result, it is probably because of your slider:
Your problem with the slider can easily be changed by placing it inside a section, but for some reason it wouldn't let me. Try getting it in a section (most preferably header section)
EDIT: If you can't get the slider into a section, then just make it from scratch.