1/ It is a nice balance between fuel efficiency and time spent aloft single engine.
( ie 1% more fuel but 5% less time)
2/ Time is a factor as per the statement above.
, since ETOPS also imposes time limits at OEI cruise speed? If so how does it play its part?
The role that time plays for OEI cruise is mainly at the planning stage. Your company would have had approval for a maximum time and then used a relatively fast speed in order to get a descent range ring of operations, that doesn't mean you have to fly that speed. The speed you do fly is up to the crew at the time ( Captain ultimately). Some companies place a maximum to aid in decsion making airborne.
For example, if you are unlucky enough to have a failure at the most critical point and then flew the speed that the company based it's EDTO application on you would arrive at your chosen field with much less fuel than if you flew s/e LRC.
Each situation will be different. If you have a lot of fuel you might want to go faster to minimise the time aloft. If fuel is critical you might accept being airborn a bit longer in order to arrive with more fuel.
Does that help?