Rudolf,
As to what is the "best time to travel" weather, check out WeatherSpark.com. They have fantastic climate data for much of the world. Once you review the data, you can decide what is best for you as what is best for me may be different.
Info regarding bikes and Amtrak is found here:
https://www.amtrak.com/bring-your-bicycle-onboard. Since I assume you are flying into the USA, you will already have a boxed bike so if you want to keep your bike boxed until you get to riding departure city, be sure that town has "checked baggage" available. Personally, if I were flying, I would try to fly all the way to the departure city as NYC would probably require an overnight stay ($$$$) and if you take a taxi with your boxed bike, you would have to get a large taxi (more $) from the airport, then still have to pay for the train (even more $). The way I am reading the website is you have a choice between carry on (hop on/off) and checked baggage for the bike. Unfortunately, Amtrak is not nearly as nice, efficient, etc. as Germany's wonderful train system. Don't judge the US by its trains!
The Manitowoc ferry is basically in downtown Manitowoc. It will not be an issue riding from the ferry to the start of the spur.
I rode another option (reverse direction) in 2020 that goes from Manitowoc south to Milwaukee on low traffic county roads and/or bike paths then head west from Milwaukee to La Crosse using mostly bike paths. At La Crosse, you would connect to the Northern Tier and take it to Fargo. This route is very similar to USBR-30. If you choose this route, I have routes I can send you with GPS data and most services listed if you want. Just private message me.
Another option is to review Wisconsin's bike maps as Wisconsin (especially the southwest or "driftless region") is wonderful to ride in. Lots of bike trails, bike routes, pretty good drivers, frequent services, etc.
Whatever you choose, I wish you a wonderful trip. Tailwinds, John