the first question is controlled by css. Look down in your css code for the #page formatting. This is down where it says "Begin Structure".
Change the margin from 20px auto; to 0px auto;
Those numbers always go in this order - top margin, right margin, bottom margin, left margin. So, basically the current code is telling it to put 20px space for the top margin.
The 2nd question I think you'd have to add an image tag in your css code too. I'll have to load up the default theme and look at it to remember.
Hope that little bit helps in the meantime.
I just remembered by looking at the graphic files included with the theme - even with a top margin of "0", you'll still have some grey at the top because it is part of how the header graphic was made. I THINK that when you replace the default header with your own though, that should go away as long as you don't add a border into your graphic. Hope that makes sense?