Copenhagen to Bacharach Germany

The train trip takes about 10 hours by day, with 2 or 3 connections, or you can take an overnight train with a transfer at Cologne about 6:15 a.m. How to Look Up Train Schedules Online gives you the DB train schedule link and tips for using it.

Just fly to Frankfurt. I haven't traveled by train on the entire route, but I have for portions. The scenery is relatively uninteresting. You're not missing much if you fly.

Definitely fly. Trains, ferries, cars, etc. are all amazingly expensive in Scandinavia. Plus it's a long, inconvenient trip unless you plan a lot of stops along the way.