The correct answers are The head chef prepared the star-squid, and the apprentice, the meteor-mushrooms and The head chef prepared, and the apprentice seasoned, the giant meteor-mushrooms.
The head chef prepared the star-squid, and the apprentice, the meteor-mushrooms.
This is a correct example of gapping, where the repeated verb ("prepared") is neatly omitted in the second coordinated clause.
The head chef prepared, and the apprentice seasoned, the giant meteor-mushrooms.
This is a correct example of right-node raising. The shared object ("the giant meteor-mushrooms") is omitted from the first clause and delayed until the end of the sentence.
Incorrect options:
"The apprentice has, the meteor-mushrooms" is ungrammatical because you cannot use an auxiliary verb ("has") to gap a main verb while introducing a new direct object.
"The apprentice has too" is ungrammatical due to a morphological mismatch. The first clause uses the continuous participle "roasting," but "has" requires a past participle ("roasted").