Please refer to the following link about how to share images on Facebook:
You can add watermark to your images while sharing as well through publishing manager, as you want your images to have your tag as owner.
There is no such way you can add watermark in Lightroom mobile
You have to use the copyright feature in the desktop version of Lightroom. Once a copyright text is associated with a sync able photo within your catalogs, syncing from the desktop to your mobile device will add the watermark to you Lightroom Mobile pictures.
Please let us know if it helps.
That answers my second question. Thank you!
Still waiting to here about album sharing in mobile app. If the share feature can't say it's from an album I created, and if I can't watermark in the mobile app, then I don't see much use of this feature for photographers. I'll just have to wait until I get home and share from the full Lightroom I guess.
You can share your collection from your Mobile app. But you can not add watermark on it from the mobile app.
Though you can share the captions, Camera and camera raw info and location info while sharing the images via mobile app.