Changing to sticky menu & customized navigation bar for mobile (Avenue Template)

Site URL: https://www.mialee.work/

Hello, 

I'm working on my web portfolio (www.mialee.work) and am running into some issues on the mobile site. I've listed changes I'm working on in order of importance and would appreciate any help and pointers. Attached is an image of the current state (top 2 images) and the desired outcome (bottom 2 images).

1. menu:
   1. I'd like to change the current mobile menu to a sticky menu, flushed right, with the very top item to be "menu" (or hamburger). Right now, it's centered and when opened, pushes the web content down and the "menu" is the last item.
   2. The menu stays open when navigating between pages on the website. I'd like this to be set to its closed position when opening a new page on the website.
2. logo: I'd like to change the current placement to flush left and in line with the menu. If not possible, I'd like to replace it with text or hide it.
3. overlap image: I may have to change the block type completely but is there a way to work around it so that the overlap image is smaller while the overlap title size is unchanged?

Thanks for reading! 

Mia