Google-photos – Merge and trim videos from Google Photos

I solved it in no time with https://app.mover.io/ (freemium. I used it once to do a massive, one-time moving)

Just authorize both apps to be connected through the web interface and you're all set! You can see a progress report and in a few hours (I was moving 7-8GB) you'll have your files transferred.

No you cannot do this on Google Photos.

--Update--
Not a chance with Google now, they are shutting down Picasa at 1st May.

This option is only available on Picasa web album. Google Drive does have an option to block the download link in the "advance" section of the share settings, and it will create a new Picasa album with uploaded photos automatically. However, you cannot edit such album on Picasa and will get a "500 Internal Server error" when you try. So you may want to upload your photos to Picasa directly.