When I go to Appearance -> Slider Admin, I add a new Slider and once I'm done I press the save changes button and then I see the green box saying Options Saved. The problem is when I refresh the page it didn't save the new Slider that I added.
Try re-activating or re-installing the theme. Sometimes WordPress fails at saving the options to the database, but I've seen others reporting this solution works. Let us know here :)
Didn't work, but I guess maybe my server was too slow and I have to give it some time so it can actually saves.
Plus, do I have to upload the pictures afterwards and change everytime the url for the thumbnails because if I don't give them any specified url, I only see the default thumbnail.
You don't need to upload pictures again if you reactivate the theme or re-install it, those are saved in the database. You only need to make sure your server works and options are being saved.