It read full tracks at a time, but you can see from the doc there were 11/22 sectors with no inter sector gaps, but there are separate sectors of 512 bytes which are addressed in the file system structures.
That's just a clash of nomenclature between the logical and physical layout. It had logical sectors, but on disk, it was written as one contiguous sector.
Yes, it read the whole track, starting from wherever the head was, then the floppy device handler figured where each logical block was, based on the magic sync word $4489 (which is not supposed to be output by the default MFM encoding) and track/sector IDs embedded in the track's bitstream.
Not even "Not supposed to be" -- it can't be. $4489 decoded is a valid byte, but with one of the clock transitions 'blanked'.
If you decode $4489 via MFM then re-encode that byte, you'll get a 1-bit difference. This is why it works as a sync marker: even if you wrote that byte in the data area of the sector, it wouldn't encode the same way because of the missing clock :)
It's a common trick on radio systems too -- a short burst of data which can't be obtained through normal encoding processes (invalid FEC bits, flipped parity, etc).