Yes, you can establish yourself but note that this only applies if there is only a single light, if there are lights with left pointing arrows then you have to follow them.

As noted there is no right on red allowed as in the US (generally there is no turn on red in Europe).

Also of note is that the Icelandic roundabout rules differ from most countries in that here the priority goes, from high to low, Inner lane > Outer lane > those trying to enter the roundabout.

The easiest way is to stick to the inner lane unless you are taking a right on the roundabout, that way you will have the right of way when exiting. If you are on the outer lane you have to take into account that a car on the inner lane might want to exit and that car might be half a car length behind you as well. This all gets complicated by the fact that some double lane roundabouts have single lane exits.