How to keep Search in Logo in Menu bar + keep it sticky

Hello there,
Thanks again for a marvelous theme. I’m using your vantage theme and I’m trying to do the following:
1. Use logo in menu.
2. Keep the menu collapsed on all views.
3. Keep the bar sticky on top.
4. Keep the search box in the menu.
I was able to achieve step 1 & 2 succesfully. However, I lose the ability to keep the menu sticky as in number 3 and also the search box disappears in Responsive mobile view. I have followed all the necessary steps to do this in your Navigation theme settings. Can you please help help?

URL: http://www.storiestogrowby.org/whootie