Can I remove the top Navigation Bar completely?

I am new to Zen - the site I am working on (very much a work in progress) is s a r a h s s o f t n e s s c o m

I was not able to get my logo to work well on top because of its shadow (the transparency looks very choppy) and I do not currently need any of the top links on the top bar (EZPages, Privacy Notice, etc).

Can I disable it completely and move the main body of the page up?

top links on the top bar (EZPages, Privacy Notice, etc).

The stock template does not have those on the top navbar, so we would need to see what you actually have before advising on how to change it.
Oops, you did show the site name... I'll look...

That is the ez-pages header nav, so you should be able to turn it off in Configuration > EZ-Pages Settings > EZ-Pages Display Status - HeaderBar.

Viola! I did it, thanks.

How can I move everything up now?

Do you play the viola? :lookaroun Your Template Monster template has lots of non-standard elements in the header, but there looks to be enough specificity to control it.
Find in your stylesheet_tm.css (line 45)

#header .row {
height:80px;
overflow:hidden;
width:100%;
}

Change the height as desired.