By the way, once such a batch automation starts, how can I stop it, so
I won't have n times the same error message?
Press ESC while the batch is running and you'll be presented with an option to continue or stop.
The action does the same thing with the dialog turned on or off.
Now I don't understand. What is producing the error - the action or the Batch Dialog?
Also, you didn't mention anything about resizing, although that shouldn't have anything to do why a destination folder is reported as not being present.
You can create an action from one or more actions as well so that you could have a Resize action, and a Save For Web Action, and combine them into a "Resize and Save" action and run that last one on batch.
In any event, I don't understand what is producing the error, the batch or the action. If you can elaborate, maybe step by step what you are trying to do, then we can peel back the layers of the onion a bit.
Peace,
Tony