As i do not have in the moment acess to pc, i will tell u how to fix that bugs, and in few days i am gonna make changes to code. It's really strange that u got that bugs, beacuse i tested code, before posting, on resolutions from 1024x768 up to 2k, and the button should be displayed somewhere on vertical middle of page, rather than where it is displayed for u. Maybe u made some changes in code, but here is fix.
In custom header find .hideb class. Under that class there is top: attribute. From 45% change that to for example 50%, which i believe will resolve ur issue, if not try 55% etc.
For second problem with links in custom header find .customlinks class and change width attribute to, 70px or 80px. Than go to css and find .Dropdown-menu--right and change left attribute from 180px to 200 or 210px.
Let me know if it resolved issue for u.