Can someone provide factual information on what is in general the SOP (if it varies) or manufacturer recommendation on an 'engine cowl release' while in flight?
There is no written procedure or SOP.
Does the engine have to shut down as precaution if there is no other indication of problem?
Of course not.
Can someone also explain what problems the cowl release creates?
Probably not - it's not something that's simulated or trained and the effects are specific to the chance circumstances at the time. I suppose it depends how many latches were unlocked and thus what speed and body angle it happened at.
Someone mentioned earlier that missing cowl disrupts airflow and can lead to engine surge.
If one of the computers (ECU/EIU etc.) is whacked or damaged in the process or something goes down the engine then it might.