Can I put a rotating ad (or maybe slider?) in the header area of my site?
Attached files: Screen Shot 2017-07-06 at 5.31.05 PM.png
Yes by filling the textarea in Miscellaneous > Top Ad Code. Since the textarea allows HTML you can potentially put anything in there.
Can I place a widget box in the header? This is advertising that we're selling privately and I don't have an html code like what Google Adsense provides
No you can't load a widget as that would require it to be a widgetized area which is not. You would need some custom coding for that.
I'm not sure what type of element you want to put in there, but if it's a static image you want to put there something like that would be enough:
<img src="http://www.dirtmonkeyu.com/path-to-yourimage.png" />
Hope it helps