Answer: Yes, in both cases.
The wooden frame is in the player's area of intended swing whether they are right or left-handed. It is artificial and is therefore an immovable obstruction from which the player may take relief under Rule 24-2b.
Question 2: In properly taking relief from an immovable obstruction may the player clean their ball before dropping it?
Answer: No, in both cases.
The wooden frame is obviously not interfering with the player's stance or area of intended swing. The Rules do not provide line of play relief, or mental interference relief, from immovable obstructions.
Note: In some tournaments there may be a Rule of Competition providing line of play relief from temporary immovable obstructions (TIOs).