Mobile view, create new menu for my Wordpress website

General information for the website: Menu evelop
Description of requirements/features: All the following is related to work I want done for my websites MOBILE responsive version. But, ideally any work that is done, I want to to not effect my desktop version... if possible.

Jobs to do...

1) Im not happy with the standard MENU/Navigation on my mobile view. I find it slow and not engaging. It also spreads too far across the page (see googled example, although my menu covers my full screen),
I want my menu/navigation bar edited so it doesn't cover the full screen. I want client to see my website under the menu at all times.. like example attached.

2) I also want several buttons/links put on my home page, so that a user can select and be navigated to any of my other pages...instead of using the standard navigation bar.

3) Whichever page of my website the user is on... I want there to be a very large obvious "back button" which will take user instantly back to home page. I would like if this could float and be visible at all times, even when the user is scrolling up and down throughout the page.

4) I have to wide photos, that work perfectly on desktop version... but on mobile version they are reduced in size so much that text written on them is not easily read. I need these two images customised to fit the mobile version.

5) I want a gallery page added.

6) I want a photo on my homepage replaced/swapped.

Some of the above will require developer experience, some will require graphic designer experience.

IMPORTANT...
When you reply, please do not just send me a standard copy & paste as that will tell me nothing about what you can do for ME. Please comment on all SIX of my problems, and what you suggest can be done to fix my SIX issues.

Sensible prices please... i have a good idea how long this should take to complete.

Thank you
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