The correct options are
A Having stolen a piece of cheese, a crow flew to her nest to enjoy the tasty meal.
B Stealing a piece of cheese, the crow flew to her nest to enjoy the tasty meal.
To express the logical sequence that is stealing of the meat followed by flying, we can use both past participle or gerund form of the verb to express participle. Hence, both A and B are correct. The rest of the options do not adhere to this rule, hence incorrect.