Keflavik Airport is fairly compact so going around should not take too long. I have only flown to Iceland from Europe so cannot say about immigration as within Schengen there is none. However, in my experience everything runs quite smoothly in Iceland so would assume that this applies to immigration and customs as well.

I have taken both the Grayline and Flybus from KEF to the Hilton and on both times the bus dropped me off along the way without need to go to their bus terminal and change for a shuttle so it is worth mentioning to them where you are going.