Could possibly be the DMF, I experienced the same issue for a few months. Once the car was idling you could hear a knocking or shudder noise also at low RPM the sound would come again. If your car is at running an idle and the sound appears try pumping the clutch in and if sound goes away its definitely the DMF (throw out bearing aka release bearing).
Regarding the cold start, my car was similar where it cranks over for a couple of seconds first before it would start even after the engine had fully warmed up the issue was there, possible solution which worked for me was when I had my car remapped the tuner added or adjusted something to the ECU called a "hot-start" and now my car starts up first time every time.
Regarding the cold start, my car was similar where it cranks over for a couple of seconds first before it would start even after the engine had fully warmed up the issue was there, possible solution which worked for me was when I had my car remapped the tuner added or adjusted something to the ECU called a "hot-start" and now my car starts up first time every time.
