tele_tubs Is it possible to hide the public sort button in the top menu?
You can just hide the button with custom CSS:
#change-sort {
display: none;
}
tele_tubs Is it also possible to have different sorting order in different folders?
No, because that requires per-folder configuration, and that would require Files gallery to work like a "CMS" and store config files inside each folder. Possibly in the future.