I will be flying from LAX to Amsterdam and then to Rome all on KLM. I will have a 2 hour and 15 minute layover in Amsterdam. If I check in a bag at LAX, will I have to claim it when I go through Customs and Immigration in Amsterdam or will it just be transferred directly to my flight to Rome?
Providing your 2 flights are on one ticket, then your bags will go directly to your connecting flight. You only need to deal with Passport Control in Amsterdam.
If you are on one ticket, it will go all the way. If you are worried, watch the tag they put on your bag at LAX should have the Rome airport code on it.
YOU will have to go through passport control at AMS, but not your bag.
No, your bags are checked through, and you will not see them in Amsterdam, just verify when they tag the bag at LAX that it says Rome on the tag (likely FCO).
In Amsterdam, you will get off the plane and be in the international terminal. Follow the signs for connecting flights, it helps to know your gate, as there are different immigration kiosks for different gates (though technically any will work). Follow the signs, get through immigration, and on to your gate. 2 Hours 15 minutes is plenty of time, I typically get through in much less than an hour.