Increase header height

Dear All,
I am a a newbie and started to build my website using sydney theme by creating a new child theme on MAMP local serer before it goes live.

I have the following problems.

1) How can I increase the height of header so that i can accommodate full size logo?
2) I would like to get rid of little white space above the header/navigation menu. This I see just on the home page.
3) How to keep the header always black in color
4)how to reduce the gap between the sentences on the first slider
5) how to add just 3 sentences (3 lines) of same size font size and a click symbol in the second slide?

I appreciate if some one helps me.

Thank you very much.
keshav