1. Yes, they are engulfed until dispelled
Nothing, not physical Objects, energy, or other spell effects, can pass through the barrier, in or out, though a creature in the Sphere can breathe there.
and a Gelatinous Cube's engulf says:
An engulfed creature can try to escape by taking an action to make a DC 12 Strength check. On a success, the creature escapes and enters a space of its choice within 5 feet of the cube.
So since a creature cannot leave ORS and ORS is around the Gelatinous Cube, the engulfed creature cannot get 5 feet away from the Gelatinous Cube and thus cannot dis-engulf themselves from it
2. Yes they can escape and prevent further damage
If the toad dies, a swallowed creature is no longer Restrained by it and can escape from the corpse using 5 feet of Movement, exiting prone.
When the giant toad dies the character is no longer restrained. By spending 5 feet of movement the character can free itself from the giant toad corpse and thus not continue taking damage. ORS does not prevent this because the 5 feet of movement does but actually move you five feet (and thus would not cause you to hit the ORS barrier), it is just a cost to escape the stomach if the giant toad. This is similar to the way that spending movement to stand up from prone does not move you anywhere but just let's you stand up.
Presumably, after the giant toad's death and having spent 5 ft of moment to escape the swallow you will be prone in the same square as the giant toad corpse, but you will not be taking acid damage. However ORS will still be surrounding the giant toad corpse (ORS can affect objects or creatures so it shouldn't vanish).