Helpdesk solution which is not form based

Is it possible within the wordpress framework to create something like what I have tried to explain above?

yes, but you’ll need to build it yourself. I created something similar for a project once using contact form 7 plugin and a custom multi-form on a slider using the multi-slide extension. You can also use the multi-page approach.

Use images as radio buttons to enable visual selections of options.

I used the Post My CF7 Form extension to save the submissions directly into custom posts in the dashboard if you need to keep a track of the help requests.

To your knowledge, has a plugin like this already been created for wordpress?

not that I am aware of and probably not in a free version.