This is a case where the one time use of an actual Windows PC will probably fix your problems.
If you want to keep the DRM in place, then setup Adobe Digital Editions for your existing AdobeID on the Windows PC and then plug in the Kobo and authorize it from within ADE. Then the Adobe ebooks with DRM should work.
If you want to strip the DRM, the first step is to extract the encryption key that ADE is using which is done on a Windows system with ADE installed. This might be possible using Wine under Linux but is easiest under native Windows. Once you have the key, removing the DRM should be possible under native Linux (it is just a python script). One issue is that you will need the latest scripts. The best single site for up to date info about DRM is Apprentice Alf's Blog.
Note that DRM always screws you if you use it long enough. So removing it immediately is always the best option. Despite what the publishing industry implies, this has no downside for the purchaser and reader of ebooks that I can see providing you only make personal use of the ebooks.
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