I don't remember how to access the storing of params in CB Activity table via an external file.

What do you mean by this? You have a Code action with Method set to PHP and you're including your own file? It's no different than if you weren't using a file except you can't use substitutions in your file. Your own topics below have examples already for using CB Activity params storage.

www.joomlapolis.com/forum/developer-members-support/245083-save-to-another-table
www.joomlapolis.com/forum/developer-members-support/244923-cb-autoaction-and-data-attributes

On a second topic I read that autoaction now supports $actiondata. Can I use this to transfer the result of an outside php file called in the autoaction to it and use this result in the following lines of the autoaction and how ?

Action data is used to add additional substitutions while an auto action is executed. Its primary purpose is to pass newly created objects to substitutions for usage in the Output tab. It's not a means of passing it wherever you like.

You're using an After trigger. That means it's after the activity was stored. You need to use a Before trigger to add data to the object to be stored. Your code is working fine it's just not storing because wrong trigger.

Then you'd be writing to the database twice for no reason. Why are you needing to do this on the after trigger? Are you needing the activity id? You can also just directly trigger a store yourself instead of writing queries. This is done by just calling ->store() on var3 like how ->params() is called.