Hi,
I can see these paths were tagged 3 years ago, but anyway:
Is it correct that it is forbidden to cycle here (bicycle=no), or is this just a confusion between access tags and something else?
In general, all the access tags (e.g. bicycle, horse and foot) are only about access. The bicycle tag is not about e.g. how suitable a bike is on this trail. That is given by other tags like mtb:scale and class:bicycle:mtb :)
Anders