Mobile Customization

I’m wondering if there is a way to have the menu always shown in the mobile version (site with width 380px). Rather than having to press the button with the three horizontal lines to make it appear. If so, I’d also like to remove that menu button also.

Secondly, is there a way to turn off the social media icons and search button only for this mobile version (again the 380px width site)?

Thirdly, my slider has white space under it in the mobile version. Any advice on how to remove that? If not, is there a way to remove the slider just for the mobile version?

For reference my website is: http://www.tanninofokemos.com/wp

Any help is appreciated! Thank you for your time!