I understand I have to go through Immigration/Passport Control at KEF, but if I'm connecting to AMS, at what airport do I have to claim my baggage and go through Customs? At KEF or at AMS? On the way back, I'm assuming both Immigration and Customs take place in CLE, right?
On the way to Amsterdam you will do Schengen entry immigration at KEF and customs at AMS (no exit check in US).
On the way back you will go through the Schengen exit check at KEF and US entry & customs in CLE.