How can I connect Indesign with Incopy? And will the texts written in Incopy be automatically synchronized with Indesign?
You have either to export text threads to InCopy Stories (Edit > InCopy > …) or you have to place InCopy stories into InDesign.
You will see InCopy content in the link panel. If they have changed you will be asked when you open the INDD file or later you can update the links like you would do if an image from Photoshop changes.
An InCopy file can be placed in several INDD documents. If you make a change it will change everywhere it is placed. To make changes from InDesign you have to check out the InCopy content from InDesign and later check in again.
InCopy and InDesign have to have the same version number to work properly together.