[Sirtel]

Kobo app is not necessary.

To have automatic metadata syncing, first turn it on in Calibre (Preferences - Sending books to devices - Metadata management: Automatic). Next, go to the Kobo driver settings (they're easiest to access if you install the Kobo Utilities plugin, right-click on the plugin icon and select Driver -> Configure current driver) and make sure that on the Metadata tab, Update metadata on the device is checked.

There's no need to run anything - it's automatic when you connect your Kobo to Calibre. When transferring new books, it's necessary to connect twice for some things (series, for example) - first, you send the books, eject your Kobo, wait until the new books have been processed (usually a minute or two, depending on the amount - you'll see it on the screen of your Kobo) and connect again. The series information is transferred on the second connection.

I don't think you can sort by publication date. However, you can make collections based on publication date in Calibre and have them transferred automatically to Kobo (again customizing the Kobo driver, Collections tab). For example, published in 1950-1959, in 1960-69 and so on, or any other combination you want.