Is it ok to freeze a chicken carcass to make stock with another time? And if so, after I make the stock with it, is it ok to then freeze some of that stock or would that be refreezing & thus unsafe?
I freeze my bones for stock as I accumulate them, keeping a large plastic bag in the freezer and adding to it. Then when I have enough, I make the stock, leaving the bones frozen. They thaw as they cook. I then cool the stock in an ice bath, put into individual plastic containers, two cups each (I find that to be a perfect amount for most recipes) and freeze them.
It is okay to freeze the bones for stock. The stock you make can itself be frozen.
Following the strictest rules to the letter, you should not have your stock, or any component from which it was made in the "danger zone" (40 F to 140 F, 4 C to 60 C) for more than a cumulative 4 hours over its lifetime. Note that this is the same rule as if you had used your carcass immediately to create stock.
It will be easy to comply with this rule, as there is no need to thaw your carcass before adding it to the stock pot. It will thaw just fine as the pot comes up to temperature.
In practice, stock is far more perishable than the items it is made from, so as long as you treat it properly in its own right (cool it rapidly after making it, as in an ice water bath), getting it under 40 F / 4 C absolutely as quickly as reasonably possible, then you will be fine (assuming your carcass had not previously been mishandled).