To estimate the VA rating one could measure the ohmic resistance. Most of the loss at nominal load is from this resistance. There are some tables how much loss a transformer of the given size can tolerate. This also depends on the temperature you want to run it. So the VA rating is not so much a number than is accurately fixed, more like a VA rating versus temperature curve. The standard rating in usually a given temperature rise.
Another way would be looking at catalog data from similar transformers. Especially with ring core, there is not that much to make different with the copper. It would be only the temperature rating that can make some difference. The 125 C look more like at the lower end.
The thermal fuse is usually one time. Self resetting fuses are rare with transformers - maybe useful for halogen lightning.