If you have a lowsec static, you should see a J244 wormhole leading to a lowsec system.
Regarding your questions, the C125 and M609 (M608 does not exists), yes the point of origin is your solar system. However, if you see the WH type it means K162 will open on the other side sooner or later.
K162 means the point of origin is the other side of the WH connection.
Regarding how spawning K162 works, see: