The logical way to do this is to have a subscription to the creative cloud. Your desktop computer would have all of your master photos on it. Then you could create collections to share via Lightroom Mobile. Lightroom Mobile could be installed on your mobile devices and any shared collections would be accessible and editable. As far as your Surface tablet is concerned, if it has a full version of Windows installed on it you could go to Lightroom.adobe.com and sign in with your Adobe ID and password and have access to those shared collections. There is no provision to have all of your photos in one location and automatically accessible in Lightroom on all of your devices.
Lightroom does not and cannot work with master photos in "the cloud". Photos must be on a local disk or on a network drive.
However, there's nothing stopping you from mirroring your photos on the local disk to a cloud drive. The way Lightroom works, if you did such a mirroring, the photos in the cloud would remain as the unedited photos.
The alternative is to publish the edited photos to some web location (Flickr, SmugMug, cloud drive, etc.), or to use Lightroom Mobile which allows you to access the edited photos from Android or iOS devices.
You do not need to gather everything to one location. You might WANT to do so for non-Lightroom reasons, and that is fine, but it is not a necessity as far as Lightroom is concerned.
My preferred organization is to use keywords and other metadata in Lightroom for all organization and searching. The file structure should be relatively simple and flat, I use folder names that are the capture dates of the photo/video. If and when you import things into Lightroom, you can create such a flat folder structure where the folder names using the COPY command and the proper options in the Import box, if you want.