For the folder tree, there's an option under Preferences / Folder Tree / Contents for SkyDrive/OneDrive. For me it isn't currently working on Windows 10, so we may need to make some changes on our side due to Microsoft changing the way OneDrive works yet again, but you should be able to hide it soon. (It may be worth giving it a try anyway, as it may turn out to work with SkyDrive Pro which you've got there.)
For the context menu, Crash, exit or high CPU when right-clicking certain files - Directory Opus Resource Centre has instructions on how you can disable certain shell extensions inside of Opus. See the Finding The Culprit and Disabling A Specific Extension. They're about disabling things causing problems, but can also be used to get rid of things you just don't want. You can ignore the rest of the guide apart from those two parts.