I have downloaded the latest version into the server, managed to download and upload the MySQL old database, copied the ALBUMS and CACHE directories from the old to the new server. Everything worked!

The issue is that although in the admin everything is working, both albums and images, in the gallery it displays only the thumbnails but when clicked it shows a wrong address. What did I do wrong?

Probably you htaccess file is wrong. Delete it, re-run setup and click on the link to recreate it.

Yes it was htaccess wrong. Fixed it now it works. Many thanks!