One of the reasons you are not finding fares is that most of your travel is outside Germany - in Netherlands, Belgium, etc. I suggest you find the national rail line sites for those countries. I'm sure someone here has them.
Basel-Kandern: One reason for your difficulty finding fares and maybe all connections is that you are traveling through two or three counties. Basel airport (Europort) is actually in Basel in a special corridor connected the city but surrounded by France, and I don't see any transport directly across the river to Germany except in Basel, Switzerland, so you will need to go by bus into Basel, then by train and bus to Kandern (it looks like Kandern doesn't have a rail station). There is a special transit district, Triregio, made up of three transit districts in France, Switzerland, and Germany. They do issue a Tageskerte for unlimited travel in the three districts for a day, but it's 18€/P. I think you can do better. Unfortunately they only seem to sell single trip (Einzeltickets) tickets for downtown Basel to Kandern, but not from the airport.
The Basel transit district, BVB, sells a ticket from the airport (zone 13 to zone 10, 2 zones) for 4,70 CHF per adult. They will probably take Euro but at an unfavorable rate and give change in CHF. That would cover the #50 bus to the SBB Bahnhof (zone 10) and a train or tram (#2) to the Basel Badischer Bahnhof (a German Rail station inside Basel, Switzerland, also zone 10). From there you can take a train to Lörrach and a bus to Kandern with an RVL (Regional Verkehrsverbund Lörrach) ticket for 4,-€/adult.
Use the Bahn website to look up Kandern to Boppard. If you put in a stopover in stopover in Worms, but don't specify "local transport only", it will give you a 5h10 connection going by bus to Basil Badischer Bahnhof (4,-€/adult), then by ICE to Mannheim and the rest of the way (Worms, Mainz, Boppard) by regional trains. I see fares for this connection as low as 59,80€ for two people. Since the trains from Mannheim to Boppard are all regional trains, you won't be held to specific trains from Mannheim on. You can stay in Worms as long as you like before going on to Boppard.