When migrating from iPhoto to Photos the trainer deleted Photos library rather than iPhotos library

After trying many different ways I could not fix iPhoto. However I succeeded to import photos to iPhoto. The trick was to run Image Capture, import photos using it and selecting the destination to iPhoto. It worked like a charm!

From Apple Support:

iPhoto automatically imports all photo stream photos into your library so you can keep them permanently (...)

Unless you disable "Automatic import" from the options, there is no need to manually copying them as they already are in your library.

Also, adding them to iPhoto albums does not make additional copies of the pictures, just lets you arrange links to the originals in any fashion you like. In fact if you remove a photo from an album:

The photos are removed only from this album, not from other albums or events in your photo library.

And neither from the library, for that matter.

This is because iPhoto albums work like labels, instead of being real folders (see an explanation here).

So to answer your question, enabling My Photo Stream on your iOS device and iPhoto, keeping auto import on, should suffice to have one copy of your pictures on your hard drive, given you regularly open iPhoto and have internet available for both (not necessarily concurrently ).

Note that videos are not uploaded via My Photo Stream, and that you may run into trouble if you take more than 1000 pictures or let more than 30 days go between each iPhoto session.

Check Apple's FAQ on the details of this limitations.

I would advise to implement some kind of backup anyway, as this scheme will at the most leave you with one —maybe two copies if you don't delete them from your iOS device. Time Machine is easy and free; for a dedicated picture/video solution check iCloud Photo Library (paid).

This information applies to the Photos app too at the moment of writing.