Is it possible to add an extra-field (eg image) and show that field not in the main content area, but in another position of the template?

Eg: when using purity iii template

[position sidebar-1]	[position component]
extra-field-image	IntroText Full Text

Yes, you can pretty much render an extrafield anywhere in your template.

Use this code as a starting point github.com/kricore/Advanced-templating-with-K2/blob/master/_inc/cheatsheet.php#L168-L173

As for the specifics of the template you need to ask the template's devs about it.