Eurail pass - seat reservations (through Eurail.com or other site?)

Yes. You must be on the DB ICE train direct from Amsterdam Centraal to Cologne Hbf. 4.50 EUR per person.
Cologne to Berlin the answer is yes no matter how you go. Same price.

Those are both optional reservations, but it sounds like you do want them. DB's web site easily sells domestic seat reservations but only a few international ones, hence Sam directing you to the direct trains that DB actually operates. It's no problem to use those with a pass. Conversely, if you miss the specified train, your pass is still valid to use and you're only out the 4.50 fee.

Thank you to those who responded to me. Another question... I saw that trains only reserve a few seats for Eurail passholders. Can I still book through Bahn.com? Does anyone know if there is a way to indicate on Bahn.com that we have Eurail passes. (I don't want Bahn.com to issue us seats meant for someone with a regular ticket. If we arrive and show Eurail passes, they may tell us we're not allowed to sit there?)

Deutsche Bahn does not know if you have a Eurail Pass, nor do they don't care. Reservations are optional, as Laura said. Most reservations are by people who bought tickets, or they may have German Rail passes, or Bahn100 cards. You are thinking of France, a whole different country, rail operator, and method of doing business.

You are referring to quotas for Pass holders on trains. That is not the case In Germany...luckily. No need to deal with that. I use Pass in Germany. When I want to reserve a seat, I reserve. When I don't want that, I don't and just board. No problems here.

You can use DB website to reserve only a seat, check the little box, "Nur Sitzreservierungen."

Thank you all for your replies! I did not realize that some countries have a Eurail quota, but others do not. I feel fortunate that Germany does not have this type of quota. I have booked seat reservations on all of my trains. Vielen Dank!

Yes, in France one might be affected by the sear quota when riding the TGV, (I have,to be sure), been affected by this when going Paris and Frankfurt using a Pass.

No such animal in Germany, which is one reason riding the trains in Germany is much less complicated. But it pays to get the seat reservation on the ICE Köln Hbf to Berlin Hbf. I've done that too from Duisburg and Düsseldorf to Berlin in the summer, expect it to be crowded.

Ditto ICE departures from Amsterdam Centraal.