Customs in Frankfurt.
 

Originally I had booked a flight directly from Chicago to Dusseldorf. Airlines changed it on me - I now arrive in Franfurt at 7:15am, and connect to Dusseldorf at 8:55 am. Did they give me enough layover time? Do I go through customs in Franfurt or Dusseldorf? I leave next week, so I really don't have options at this point to change the flight.

You go through immigration (not the same as "customs" - but probably what you mean) in Frankfurt. I haven't been through this airport, but from my research Frankfurt is pretty efficient and if your inbound arrives on time, you should have plenty of time. If you are worried, look to see if there are later flights to Dusseldorf after the one you are booked on, on the same airline; if there are, almost certainly you'd just get put on the next flight if you miss your connection, and because you arrive in the morning, at worst you'd just get in a few hours late.

If I have a checked bag, will I have that in my possession as I go through immigration, or will that be forwarded on to my connecting flight automatically?

You check your bags through to Dusseldorf which is where you go through customs, although customs in Europe is seamless. Simply go through the nothing to declare line and you're done.

You'll go through immigration in Frankfurt where your passport is stamped and will most likely have to go through security as well. An hour and 40 minutes is plenty of time. If your plane is late arriving (doubtful) then see any airport personnel and explain that you have a short time to connect with your next flight and ask them for help.

The checked bag is checked through to the final stop on your ticket. You go through customs at that time. Immigration in Frankfurt has a German efficiency so you should be good.

Customs is irrelevant unless you have something to declare. It's immigration you have to worry about, and it can be fast or slow. Frankfurt is a huge airport. You may have to hustle to get to the next flight.

Immigration (people entering the country) will take place in Frankfurt and that what can be time-consuming - depending on how many international flights land at one time. I would assume your luggage would be checked through to Dusseldorf - but you need to confirm that with your airline now.

Frankfurt is a large airport and you don't have a lot of time for the change ( planes usually pull back at least 20 minutes before the departure time) but should be OK if your incoming flight is on time.

As long as this is one ticket - they are responsible for getting you to Dusseldorf on the next available flight (meaning one with seats open).

Customs is a non event - you just pick your luggage off the carousel and walk out the Green - nothing to declare - lane.

Thanks everyone. You have eased my mind. I'm not an experienced world traveler, so just wanted to be mentally prepared in advance as to what to expect.