From which directory should I run those commands? /volume1/web/osticket/ ? Or only the upload, or osta?

/volume1/web/osticket/

I changed the permissions. Got a lot of errors saying that permissions couldn't change, for example on the Attachments directory.

When I delete the old logo it asked:

remove write-protected regular file?

Not sure why it was write-protected. I removed it and tried to upload a new one. which failed:

Unable to upload logo image: Unable to write to://osta/uploads/Code54_osTicket.jpg

The fact that you have an attachments/ directory tells me that you are using the Attachments on the Filesystem plugin. Not that this makes any difference to the topic at hand; it is just a note.

I'm not sure why you are ending up with write-protected files. I haven't heard of anyone running into this before. In fact, a search of this forum for the term protected only turns up one result... this post!

So I believe we've found your issue. You seem like you know your way around the Linux command line. As you actually have access to your own installation you are in a better position to figure out a solution. But if you want me to do some research and throw out a couple of suggestions, let me know!

Actually one thing that does come to mind is a possible ownership issue.

Make sure the uploads/ directory is owned by the correct user*:

# chown -R thecorrectusername uploads

*(On a regular web server I would suggest that the correct user is the same user account that the main website runs under. Of course, this doesn't really apply to a Synology NAS so I'm not sure what to suggest in this instance).

I hope that this helps! Let me know.