Customs in Frankfurt Airport

That does sound like enough time, as long as your plane lands at 8:45 as scheduled. We arrived at Frankfurt at about that time a few months ago, also without checked luggage, and it took us about 45 minutes to get through customs. Since the train station is connected to the airport, it didn't take long to get over there--although to be safe we didn't buy tickets until we go to the train station. Good luck!

Being technical, it is passport control that is the issue. Customs is whether you are declaring any goods, which usually means walking out the 'Nothing to declare" door.

Are you looking to buy a Super Sparpreis discounted ticket? Walk up fare is 74.40 EUR. With SuSp tickets going for 14.99 EUR 2 months out, probably worth the gamble. The next direct train is an hour later if you miss it.

Did you look at booking a RailnFly Ticket, That includes free use of any train after you land.

Things could go very wrong or things could go very well. One never knows for sure. It appears that you have plenty of time if everything works like clockwork and some time to spare. I would certainly plan for that direct ICE train.

Sam nailed it. Customs time is irrelevant. You can't predict if you will arrive on time or how late. BTW, in 14 arrivals in Germany, customs has never been an issue.

A Rail&Fly ticket, if you can get one, is the best option.

It looks like the fully flexible fare to Nürnberg is about €88. With that fare you can board any train to Nürnberg, whenever you arrive. Buying a cheaper Sparpreis ticket is a crapshoot; arrive too late and you lose your ticket. I would never plan on using a discounted, advance purchase ticket on arrival to Europe after a trans-Atlantic flight.

There is a direct ICE train that leaves at 10:35 that morning. Is nearly two hours enough to get through customs and to the train?

To answer the main question: yes, shall be enough time. Sometimes also the ICE trains come up to 6 minutes late.