single pilot operations, such as "flying Wild Alaska" can those pilots give flight instruction while carrying pax? cargo?
That was probably just IOE after the crewmember successfully completed a 135 checkride (135.293, .297, .299).
In terms of your question, I would imagine the answer is no unless the crewmember receiving instruction is a qualified pilot for the operation but I can't find a reference. I know we do not provide instruction to qualify a crewmember on live 135 legs at work.
I used "Flying Wild Alaska" as an example, the single pilot ops do not require a second crew member.
My emphasis in bold. If the pilot is employed by the certificate holder and is qualified in the aircraft, he/she may manipulate the controls and receive dual instruction during a flight conducted under part 135. Note there are some other provisions of part 135 that prohibit crewmembers with less than a certain number of hours in type to manipulate the controls during takeoff or landing.§ 135.115 Manipulation of controls
No pilot in command may allow any person to manipulate the flight controls of an aircraft during flight conducted under this part, nor may any person manipulate the controls during such flight unless that person is—
(a) A pilot employed by the certificate holder and qualified in the aircraft; or
(b) An authorized safety representative of the Administrator who has the permission of the pilot in command, is qualified in the aircraft, and is checking flight operations.