Yes. You should absolutely provide feedback from a save button. Word does provide feedback from the save button, but you may never notice it in most normal cases. On a long save operation in Word, you will notice a message in the status bar and the user is prevented from making changes during the save operation.
What is the purpose of Save button?
Save is writing data to a storage medium, such as a floppy disk, CD-R, USB flash drive, or hard drive. The save option is found in almost all programs commonly under the "File" drop-down menu or through an icon that resembles a floppy diskette. When clicking the Save option, the file is saved as its previous name.
Where do I put the save button in UX?
Considering that your users will typically navigate to one category, make a change, then click Save Changes, I think placing the button at the bottom/left is best. If your users were frequently making changes across multiple categories, then you'd have a good argument for placing the button at the top.