You can. Follow this guide first getk2.org/documentation/tutorials/templating-with-k2-and-the-concepts-of-sub-templates to create your own set of overrides for K2 within your Joomla template.

Then edit the itemform.php file and as the contents suggest, copy the HTML from K2's admin files. The do whatever you like with the form HTML.

But! Because the form posts data that may be required, I would strongly advice using CSS only to show/hide content. You can move code blocks around if you like, but don't delete them.

This is normal. When you place your own k2.css, K2 ignores its default CSS file. Your best bet it to copy the default CSS file in K2 into your template's /css folder and then modify it at will.

Sorry, my mind is racing...

I was referring to frontend behaviour in general, not frontend editing. It's best load a separate file or your rules in a <style>...</style> tag to overwrite default backend K2 CSS.