When editing a photo with Photos, the original is kept. Does it mean that the photo is stored twice on my hard disk? Is it taking double space (or similar)?
The edits you are doing from the adjustment panel in Photos will require only the additional storage for the new thumbnails or Previews.
But you will need twice the storage , if you are using photo editing extensions or an external editor called from "Image > Edit with -- " in Photos. The reason is, that Photos cannot recreate the edits done by the external editor or the extension, so Photos have to store the phot returned by the external editor in addition to the original it sent to the external editor. Be frugal with editing in external editors, if you want to save storage.
Luckily, the adjustments in Photos are so versatile, that I do not have to fall back on external editors too often, so it is not a big problem, that Photos will have to store the external edits as an additional file.