Am I correct in thinking you intend to mostly follow the golf tagging with the exception of the big areas that are less defined in disc golf?
RE: 1): If you’re creating a relation per item 3 then double tagging the course on the node is violating One feature, one OSM element which is a long standing principle in OSM. Overlapping areas happens all the times and generally doesn’t cause issues unless they share the same key. The concern about vaguely defined areas does sound like a good reason for avoiding area tags outside a dedicated course though.
RE 2): I think this goes against the “name is name only” principle OSM generally holds without a strong rational (sport is adequately tagged). It should be named according to signage and how it is referred to locally. Third party databases re generally no acceptable sources and aren’t relevant to OSM’s “on the ground” principles.
RE 3): see notes about name for item 2, invented names for convenience in the database is generally discouraged. If they need to be augmented for display this can occur in software.
RE 4): The usage for website is already well defined. If there is a signed website or one run by the operators then that should be the one used, not a third party’s.
There are very strict Import guidelines for this sort of thing that must be followed.
I don’t think this would succeed on OSM’s general policy on copying other maps and for similar reasons to the ban on info from Google. According to the UDisc terms:
Content on the Service may not be used, copied, reproduced, distributed, transmitted, broadcast, displayed, sold, licensed, scraped, or otherwise exploited for any other purposes whatsoever without our prior written consent. We reserve all rights not expressly granted in and to the Service and the Content. You agree to not engage in the use, copying, or distribution of any of the Content other than expressly permitted herein, including any use, copying, or distribution of User Content obtained through the Service for any commercial purposes.
I’m no lawyer, but that seems fairly clear on the “no reusing our stuff” front and if they’ve built a business around this data then the chances of them changing their mind and giving it away for free seem … slim.