I usually don't comment on itineraries, but I must agree with others have said. Here's yours with some notes and questions.
Day
1 leave -- from where? When?
2 get to Paris early-adjust-slow sightsee -- Night 1 in Paris.
3 Paris -- Night 2 in Paris.
4 Travel toAntwerp PM -- Night 3 in Antwerp.
5 Antwerp-visit friends -- Night 4 in Antwerp.
6 Travel to Amsterdam early -- Night 5 in Amsterdam.
7 Amsterdam -- Night 6 in Amsterdam.
8 Travel to cologne -- Night 7 in Cologne.
9 cologne -- Night 8 in Cologne.
10 Travel to zurich,Lucern as early as possibly. Sight see late afternoon -- Night 9 in Lucern.
11 Lucern -- Night 10 in Lucern.
12 Lucern much of the day then Head back to Zurich -- Night 11 in Zurich?
13 Fly out of Zurich -- Next day?
14 get home -- Same day.
I totally get the concept of seeing the countryside from the train, but when you use the DB website to check schedules, be sure to note how long the journeys are, how many train changes there are and click on the details and the map view to see the exact route for the options of interest to you. You may not be able to buy your tickets from DB, but you'll see the best information otherwise. You need to keep in mind that it's not the same as driving. It's often faster (I love the 250+ kph trains ), but you are limited by the schedules. If you plan far enough ahead, you will be able to get substantial discounts on fares.
I tested your longest journey from Köln Hbf to Zürich HB for 8 May. There are 1 train change options that take only about 5 hours. The change for Zürich is usually in Basel and the options usually combine a fast ICE train with another type of train. You have 20 minutes to make the switch. This is a journey that you could buy through DB, and prices are shown. When you do your checking, you'll see a wide variety of prices for different times of day and numbers of train changes. The earliest arrival in Zürich I saw was 11:00. It leaves Köln at 05:55, has 2 stops and the price is 39,90 EUR.
I asked the "when" question above because the time of year you go will have a big effect on how you pack and how much you'll see from the train, as will the weather.
This appears to be your first trip, so I also recommend that you thoroughly explore the Travel Tips on this RS website.
With only 11 nights in Europe, I'd skip Switzerland and concentrate on the Netherlands, Belgium and Paris, but it's your trip. Switzerland is expensive and CHF is the currency, not EUR. Today the exchange rate is at parity, $1 = 1 CHF, so at the moment it's easy to calculate and to compare to US dollars.