That is in fact a freeze plug. I would be concerned about the entire cooling system if a freeze plug has rotted thru.
The snapped off easy out could be cut out pretty easy with a dremil and tungstun carbide cutter. It will rip right thru the hardened steel easy out. they come in both a flat tip and a rounded nose cutter. I would suggest the rounded nose and slowly work it so you do not slip and gouge the intake.
Got the freeze plug out, punched it back, then pulled it out. It wasn't THAT easy, but for the sake of time that's pretty much what I did. Not knowing the size I needed, I guessed on a 1.5 one, because that's what it looked like to me. Seems I was right, kind of. Parts store didn't have the universal one in my size, so we went with the silver dollar ones. He brought me a brass one and I really didn't like the idea of that, my experience with brass is that it smooshes real easy and not worth it. He had one just like it in steel, and then a deep well one also in steel. I bought them all.
Started with the brass one, against my better judgement. Not having the handy dandy swivel tool to put them in with, I used a 1" socket, a swivel, and a couple long extensions to beat it in with. I didn't get it perfect all the way around, but I figured it was close enough. I was wrong. Had a bit of a leak when I first started it and when I revved it, it blew the damn plug out! I went to put it back in and really beat the sucker in this time. Ended up punching it THROUGH the hole and it dropped down in the block. Panic ensued and nearly burning my fingers off on the exhaust and the hot coolant I gave up and did some searching. Alot of people say just leave it in there, happens all the time. Some people say get it out at all costs. The cost would be taking the motor apart. I'm not doing it. I went with the deep well steel one and it seems to be holding. No leaks, no blow out.
Unfortunately now I have no damn oil pressure. Had it when I started the truck, after about 20 mins of running it, it dropped to nothing. It's always had low pressure, now it has none. I've tried draining the oil and using wire through the drain port to scrap the pickup, adding a quart of transmission fluid to clean things out, and revving the engine and driving it to try and loosen things up. None of it works. I put in 14 hours today working on this bucket, I'm gonna call it a day. Next step will probably be to take off the intake and distributor cap and jack the motor up high enough to get the pan off and inspect the oil pump and pickup. Hopefully it's just gummed up. Did have an old grand prix that sheared the end of the distributor shaft off which caused the oil pump not to work though. Hoping it's not that.