Full screen but limit height

1. I am trying to make my slider stretch all the way across the screen like in 'full screen' but I need to limit the height to 300px. Is this possible? I have multiple Sliders and I only want to do this on one or two Sliders, not all of them. Also, if I choose the 'full screen' option, if I resize the browser, there is a lot of blank space below the Slider. How can I fix this? What also makes it a bit tricky is that my menu is to the left, so if I choose other options, part of the slider is hidden under the menu. 

2. On the mobile site, the logo moves to the middle of the screen, which is what I want, but there is too much blank space underneath it. How can I change this? 

The website is:

Jess