Jens,
At least of few of your questions can be answered with the Canvas API Docs.
I am not sure about the answer to 1, though I have never seen any options like that in Canvas.
2) Depending on the logs you want, there are several API endpoints that might help (mostly Analytics). If you have access to Canvas Data for your account, then there is even more available.
3) There is an RSS feed of Canvas Status
4) Canvas supports OAuth
5) I agree that Canvas field naming for POST and PUT requests seems incorrect. However, the prefix is always the name of the resource (e.g. user, course, enrollment) so it is fairly easy to handle in your own code.
I hope this helps!