Update: answers
Are there any other relations except 18560 and 13288 marking the Euro Route R1?
Answer: see Euro_Route_R1#Relations
Why are there two relations of exactly the same thing?
Answer: the more recent relation 18560 had been tagged as EuroVelo2 before being changed to R1. Both are identical in Germany (not in other countries though).
See Euro_Route_R1#R1.2C_D3_and_EV2
Is there any reason why those two stop exactly at the German borders even if the real route covers many other European countries?
D3 (rel 13288) is a German national route. The other one should be merged into 13288 anyway.
Is there any better name than just "R1" or the German names "D3" and "Europaradweg R1"? What makes it even more complicated is that there is another bike route named R1 in Hessen, Germany which does not have anything else in common than the name and the vehicle.
Original name: R1 (regional route 1), later named "Europaradweg R1", translated "Euro Route R1". Short name on signposts: "R1".