the fetus is in the yolk sac

It appears after 22 days of pregnancy. It comes from primary yolk sac. Primary yolk sac gets enclosed inside from folding of the fetus, the rest is secondary yolk sac, which goes down to mesoderm and shrinks.

You should be able to see the yolk sac at 5 weeks.

The yolk sac eventually becomes part of the embryos midgut and is not part of the amnioyic sac. They are separate structures. It is possible to have an empty amniotic sac called a blighted ovum but it is not possible to have a yolk sac but no amniotic sac.

A yolk sac is a sac attached to an embryo, which provides early nourishment for bony fish, sharks, reptiles, birds, and primitive animals.