Sorry what model phone and what version of iOS?
It's an iPhone 5 running iOS 9.0.2.
OK first update to 9.1 then see if the problem persists... it is hardly ever the battery usually the sofware..
Ok, I'll update to 9.1 today and then see what happens after it has set tonight off the charger.
By closing all apps, except for the alarm clock, and pushing the off switch, have I been doing everything correctly in order to avoid draining the battery during the night?
That depends. We will look if the problem persists
Ok, I'll let you know tomorrow what happens to the battery charge after tonight.