Train Ticekts

For this trip I would say you are better off to purchase point to point tickets

For Amsterdam to Ghent & Ghent to Cologne:

https://www.thalys.com/de/en/

or

https://www.trainline.eu/

The trips within Belgium can be done on regional trains with no advance purchase or you can purchase in advance via trainline

Or use the Belgian railways. For the international trips advance buying might give you discount. For Amsterdam to Gent you have the choice between the Thalys and the Intercity services to Antwerpen, where you have to change. The Thalys is one hour faster. For Gent choose »Gent-Sint-Pieters«, which is the main station.
There is no need for advance buying in Belgium. Just walk up and buy your ticket. These trains run very frequently.

If you are travelling with other people it may be worth getting the Belgian Rail Pass. This gets you ten one-way rail journeys within Belgium for 77 euros, which may be shared between more than one person (so if three people travel, that uses three journeys of the ten on the pass). It is not valid for international journeys to or from the Netherlands or Germany, or for high-speed ICE or Thalys services between Brussels and Liege or Brussels and Antwerp.

Thanks for your reply. I will be travelling with my husband so will buy the Belgian rail for our day trips to Bruges and Brussel.
I would like to ask regarding whether is it better to rent a car for 4 days while in Germany rather than taking local train.
From Cologne, is it worth visiting Heidelberg for 1 night then go to Rothenberg for 1 night and drive to Fussen to see
the Castle and stay there for 2 nights prior to returning the car in Munich? Will be in Munich for 2.5 days. Or should I just
stay 1 night in Fussen then head to Munich?
What Autobahn would I need to take, would like the faster route than the Romantic Road which is slower.

For driving from Köln to Rothenburg odT, you would take A3 to A7. A3 roughly parallels the Rhine until you reach the Frankfurt area (although you can't see the river from the Autobahn) and A7 parallels the Romantic Road . Rothenburg is not far off the exit (Ausfahrt). You would continue further along A7 to Füssen.

If you decide to visit Heidelberg, the route is A3 to A5. From there to Rotheburg, you could take either A5 to A6 to A7 or drive back north along A5 to A3 to A7. Or, for a very scenic drive, follow the Neckar river upstream from Heidelberg to Bad Wimpfen, and grab A6 near Heilbron. There's so many attractive towns and castles along this route that seeing Rothenburg afterwards will probably feel redundant (other than all the trinket shops). If you have the time, Heidelberg and the surrounding area are definitely worth the visit.

Take care with the spelling: Germany also has a »Rothenberg«. You want to go to »Rothenburg«.