1. Freeze plug IS a misnomer. They ARE for removing casting sand, nothing else. The fact that they do sometimes pop out when the block freezes is just a coincidence. In many cases, the block also cracks.
2. The strap with the threaded hole will have a bolt from the outside threaded into it. When you tighten the bolt it compresses a block of rubber between the 2 sides and causes it to enlarge in diameter and basically jam itself in the hole through expansion. Replacements are available at any online tractor parts place, or TSC, etc.
3. Yes, they do make threaded block heaters for threaded holes. I have a Ford 3000 diesel, with just such a hole and block heater. This type is the best IMO and will have a hex protrusion on the outside that a standard SAE socket will fit on. When I overhauled mine in 1982, I installed one. The threaded hole had a steel plug in it from the factory with a 1" Allen head socket. I had to make a tool to remove it because I couldn't find a hex wrench that large anywhere. Thankfully I sealed threads with either teflon pipe seal or maybe it was anti-seize compound. But, when it finally burned the element in two, 30-some years later, I simply unscrewed it and screwed a new one in it's place.
Glad you got it out. Good luck with the replacement.