Is it possible for me to send what I'm currently watching as a stream to a friend at a different location, so that we can watch stuff together?
No. At least not without getting into a rather grey area that may come under our
piracy policy (wiki) depending on exactly what was being shared.
What if it was just home videos that I wanted to watch together with far away family members?
Kodi doesn't know what the media is and where it came from.
So if we made it possible for your legitimate usage case we'd also be making it for the rather more dodgy one.
What you're looking at could possibly be done via uPNP if your networks were suitably linked together, but not for simultaneous playing (at least synchronised).
Actually there is, it called cable tv.