Then this is not related to K2.
Disable other extension one by one to find which is causing this issue.

Thank you for trying to help me and time to do so.

I just deactivated all my extension except the important and K2 one, and I still have the local file that doesn't exist message.

Can my issue could eventually come from my restoration with akeeba backup? I had not this issue from my localhost??

I had not this issue from my localhost??

I am assuming this is a typo, so it is really possible.
Try using your FTP client to see if the actual file is where it should be.
If it is (a longshot) make sure that your file/ folder permissions are properly setup. Admin Tools will help you perform this task.

Ouch, after hours looking around, I've finally found the culprit, it seems I had this issue because I chose to apply a memory limitation for image treatment in K2 image parameters. I leave the filed blank and I can now upload and add item from article.

Thank you for your help and time

I 'm glad you sorted it out Quentin.