We just moved in to a house that was built in the early 90s and this is what I found in the network panel.
This had to be for analog phone service back then. Is it possible to terminate these cables with RJ45, then install a switch to get whole home Ethernet?
Yes it is. Did in our apartment a few years in a brand new build that had this same crap while all the jacks were properly terminated for ethernet. I would check your jack terminations since they might have all 4 pairs and be tia a or b and be okay. If the wires are out of order that doesn't matter is you do the same thing on the patch panel side as the signal doesn't know what color the wire is--will just seem off to someone who only goes 'by the book'.
You can replace those panels with ones designed for ethernet and re-sell the old ones as AMP is a very reputable company. Then you will need a switch there for all the ports to be usable.
I think the cabling should be good for not only gigabit ethernet, but maybe even 2.5Gb as my parents 1990s house has some of this same stuff and it's fine for gigabit if terminated properly and not untwisted too much.