715 AM flight on a Monday. Driving from Reykjavik city. I'm assuming drive is 30 min, car drop off, then customs the the gate. Thanks all in advance.
You are flying out of KEF as that is the international airport. Reykjavik is just a regional one. KEF is a good 45 minutes from Reykjavik so you need tallow more time. Security can take a bit there and the gates are usually chaotic. I would arrive at the terminal no less than 2 hours before the flight.
As stated, your flight to Berlin will be at KEF (Keflavik) airport and not Reykjavic City Airport (RKV).
Give yourself more than 45 minutes to drive to the airport as you also have to return your rental car.
There is no customs departing Iceland nor will you go through exit immigration. Both Iceland and Germany are in Schengen. But, as mentioned, security can be backed up.
For a 7:15 AM flight I would plan to leave for the airport around 4 AM. Just make sure the rental car agency is open that early. There are numerous self-check in machines if you have checked luggage and/or need to get a boarding pass.