The collections column in the device list is not editable for Kobo devices. There is a "Manage collections" option in the menu which displays a list of collections, but, changes made in it are not made to the device.
The collections shown are made up of collections on the device plus some virtual collections. The virtual collections are based on the filters and status you can see on the device. "Im_reading" is for books shown in the "Reading" filter, "Read" is for "Finished" and there are virtual collections for other things such as books borrowed from Overdrive or books loaded from Dropbox.
For the reading status, you need my
Kobo Utilities plugin. It can get the reading status from the device. Similar questions have been asked recently. I suggest looking at
Transferring books from Kobo Aura H2O to Kobo Libra H20 for some discussion on this. If you have questions after reading that, ask away here or in the
Kobo Utilities plugin thread.