Header logo size & positioning

Hi

I had a previous support thread but it seems to have slipped through the cracks as no reply after 4 days
support/topic/header-help-please/

on this site
diamondbeachresortnsw.com/wp

The client wants a burger menu all the time
I’ve used a plug-in to create the menu and it seem to work fine

I’ve also used the “Extra Content – phone number” to add a booking button top right

the problem is now with the layout of the header – a few issues
– I’d like the book now button to be at the right edge of the page similar distance form the edge as the menu is on the left (not in 20% or so from the side of the page)
– I’d like the logo to centre and be larger
– I’d like to remove the 2 grey lines and blank white panel that is pushing the page content down from the header

I’ve used a bit of CSS to get it to this stage but can’t seem to work out why the logo is so small and the left
nor can I work out (by inspecting the page in chrome) what the name of the blank panel is so I could hide it
I tried

#header_main_alternate  {
	display: none !important;
   }

which removes part – but then it makes the sticky menu look weird

I hope you can help me out ! ;-)