1) Check in Theme Options > Logo Options, you can reduce the top/bottom padding for the logo there – this will affect the header height.
2) Here is the code used for that slide content:
[sf_button colour="black" type="bordered" size="large" link="/porter-demo/product/bella-desk/" target="_self" icon="" dropshadow="no" extraclass=""]LEARN MORE[/sf_button] [sf_addtocart_button product_id="117" colour="black" extraclass=""]
3) Unfortunately not as of yet, those are custom designed svg animations. Maybe something we can look at providing in a future update.
– Ed