Repeaters are required to transmit the call sign at the end of a conversation and every 15 minutes while in use. Most don’t transmit their call every 15 minutes when not in use because that would be annoying to anyone who monitors the repeater.
So, after a repeater has been on standby for awhile and someone tries it or kerchunks it, many repeaters will issue their call sign.
As far as what inverse and normal means, DCS is a digital code rather than a tone like CTCSS. So it’s really a series of 1s and 0s. For instance 5 is normally 00000101. If you invert it, it’s 11111010.
Often, DCS codes are expressed with either an N or an I as part of the code to denote whether it’s Normal or Inverted. If neither is included most of us assume N for Normal.