How urgently should this joist be looked at by a pro?
I would get a General contractor, if you can’t drive a couple of nails or screws.
As far as urgent , probably not at all urgent.
I would want some joists hangers on the ones hanging down and only toe nailed.
the long horizontal split no worries there if you want sister if not every house has those.
The last one with the knot and split maybe sister but it probably has been like this for decades.
Do you need someone else to do the work NO.
Every old home I have worked on has very similar things that because of the quality of the wood is not a problem.
Horizontal splits I don’t even think about if the split runs at an angle in the center of a joist sure sister it. A simple car Jack to put a bit of upwards pressure then nail or screw the sistered board to the split one, if you can extend the new board ~3’ past the break out point.  Don’t push up too hard or you can create other problems.
These are easy repairs and based on taking down the old plaster you probably have the skills necessary to reenforce your areas of concern.