Can I set a Filter so that when I apply a specific label to an email in the Inbox it is forwarded to another email address? Example: If I label an email "Important",can a filter also forward it to a another inbox?
Filters can do multiple actions at once so, yes, you could create a filter that marks certain messages "Important" and forwards to a specified address.
However, filters only act on messages as they are received. You can't manually add a label/status and have a filter pick up on that to send the message.