"Radroute" is just a generic term pointing to a major way for bicycles.
In this place near Reschen (South Tyrol) it most likely points towards a stretch of Via Claudia Augusta that follows the valley of the Etsch river towards Meran:
Another map with the route can be found here: https://cycling....
It's hard to give a general answer for any EuroVelo bike path in Germany.
Last year I followed EuroVelo 2 (or EuroRoute R1) from The Netherlands to Berlin. It was reasonably well marked, but better in the more touristic areas than in the remote parts. A few times I lost the track and needed my guidebook and GPS track to find my way back.
My guess would be ...
I have heard there are direct buses connecting the Munich airport with the city. These buses might have a luggage compartment in which you could put your boxed bicycle. You can check this: https://www.airportbus-muenchen.de/en/
A boxed bicycle is bulky luggage not approved for transportation on the S-Bahn. While you might get away with it you should rather not count on it. Staff will have the final say on each individual case.
The MVG - operating Munich's S-Bahn - states (source, emphasis mine):
Für die Beförderung in unseren Verkehrsmitteln zugelassen
With limitations, you are allowed to take the bicycle on the train, but I would not count on being able to bring the box if the bicycle is still packed, since it exceeds with large margins the allowed luggage size (no side longer than 90cm). If the bicycle is packed in a box, it might even be somewhere between very difficult and impossible to get it down to ...
After some research, there are no rental companies that do this. You would be better off buying/shipping a bike or renting a car. Alternatively, as mentioned in the comments you can ship it back to the rental company but hiring a car would be easier and cheaper.
This is a local train, so given space is available on the train on the actual day of travel, you can take your bicycle. The space is limited so it could fill up, which is why there is a notice on the timetable to that respect.
Whether you need to pay for your bicycle depends on the local regulations, but these are always the same regardless of what time ...