Component can be configure to show event's for each post in blog. In such case clicking on event will redirect to post's page.
Technically it possible to assign any extra info or onclick actions to the events in scheduler, but it will require manual modifications in plugin's code.
Can't we just add a 'click here for more details' in the lightbox that would link to the post ? I guess this wouldn't require a lot of extra modifications in the plugin's code.
There is no technical problems, but I'm not sure how it can be done in configurable way - there are a lot of parameters which can be configured for new post in blog. Is creating of dummy blog post with same content of event will work in your case?
That would be a good start. I'm not asking to replicate the whole admin user interface of WordPress outside of the admin area, but creating a dummy post with the content of the event would be already awesome (and eventually choosing for a category at this stage already).
Afterwards, we can still edit the tags, edit the categories, edit everything we want in the admin area.