Has any actor won both best actress and best actor awards?

No. The only well known actor that has transitioned is Elliott Page. And he wsa nominated but di dnot win an Oscar.

No. As of 2022 the academy still uses the term actress.

Robin Williams in Mrs. Doubfire.

Dustin Hoffman in “Tootsie” would have been a good choice.

Martin Lawrence in “Big Momma’s House”.

Tyler Perry’s “Madea” is the best of the best! HA! So funny!

Actors and actresses receive the award appropriate for their sex, not for the sex of the character they portrayed. Example: Robin Williams won Best Male Performance for his work in Mrs. Doubtfire (1994 MTV Movie Awards).