Amphibians are produced externally so they do not get proteins and ATP from the mother during their maturation and differentiation. This means that they must have some way to get those things to protect themselves and survive.
The way that they get these things is yolk. Amphibians start to have yolk-filled endoderm during blastulation, [page 9, Gilbert, Developmental Biology].
I am considering the frog here as an example of amphibian. To know that things need energy to survive and that they must get it somewhere, you can deduce this solution. So nutrition and external "hatching" or development outside of female is the key here.
The overall answer to the question:
The organism must have a yolk sac, since it has yolk.
The second question seems to be an idealized one.
Without blastocoele but with yolk-sac suggests me that the blastocoel has developed already to yolk-sac. If that is the case, then I would call the thing gastrula, since for instance some species' ectoderm develops into yolk-sac. I assume that the question refers with "yolk-sac" to complete yolk-sac, not to the developing one during gastrulation.
If it is about developing yolk-sac, I would say that the cell is still blastula but is developing to gastrula. The yolk sac is not ready until gastrulation is complete.