adding a exception rule to do not disturb? I talk to a quite a few Americans, I my self am English, they message me during the night but, I do not want to switch off notifications for that Skype chat, otherwise as always, I will forget to switch it back on, and will miss something... 

Can kind-of rules be added to the do not disturb? 

or is do not disturb do not disturb at all regardless.
The only exceptions to Do Not Disturb are calls or texts from individual contacts that you have marked with Emergency Bypass. (Edit a contact, tap on Ringtone or Text tone, then enable Emergency Bypass at the top of the screen. You have to do this for each of calls [ringtone] and texts [text tone] if you want both to get through.)

You cannot add exceptions for any other kind of notifications or activities.