Will this cable work also with the InternetBox3 and the upgraded speed for 10gb? or, do I need to use the cable that has the red-end?

Yes, you can connect your Internet Box 2 to your OTO socket with this cable. If you look at the back of your Internet Box 2, you will see an SFP with a blue bracket (https://swisscomvbc.scene7.com/is...), where you plug in the side with the blue connector. The OTO socket should have a green socket and you connect the green end there.