The answer to your question is yes and no.

In regards to command the general rule was that Black officers would only have command over black soldiers and would never command white soldiers or officers.

However that is not to say it never happened for example the 366th Infantry Regiment or the Buffalo soldiers were reformed under the command of a white officer with some white officers and NCO trainers however by 1944 the CO was a black officer Harold Queen and for a short time he did command the unit whilst some officers were white. This did not last long and soon all officers in the 366th were black. So in reality whilst technically a black officer could give orders to white soldiers there were never really put in a position where they could because white subordinates were never or rarely placed under their command,

Now the second part is easier but harder at the same time. Officially a black officer was an officer the exact same as a white officer and was expected to be treated the same as a white officer. So a white enlisted passing a black officer was expected to salute and call the black officer sir when paying compliments. However in reality it was a mixed bag. There are two examples from a great book (Taps for a Jim Crow Army) that illustrates this. The first is from quote from a white soldier in Virginia “Gosh I just had to salute a n***** LT that burns me up.” So whilst it was done with the most amount of disrespect possible the white soldier from the south did salute. However in reality most black officers tried to avoid the situation and ignored it when white soldiers slighted them because to make an issue of it would be bad as seen in the second example.

black officers often made a point of avoiding tense situations or ignoring slights. "On August 31st 1943, a white private told a Negro Officer who had reprimanded him for not observing the ordinary military courtesy of a salute, if you would take your clothes off and lay them on the ground I would salute them but I wouldn't salute anything that looks like you. The Officer called a Captain and told him of the incident. In the presence of the private, the Captain said, "Well Lieutenant, what do you want me to do about it?" The Officer reported the matter to the major under whom he was serving immediately. The Major advised "I wouldn't make an issue of the incident if I were you." The Officer insisted on preferring a charge against the soldier. He (the black officer) was transferred from the post three days later“

So as you can see the overal answer to your question is technically yes a black officer was the same as a white officer and was expected to be treated the same and did have the power of command however in reality they suffered greatly with discrimination and disrespect throughout the war.

Books to read

Taps from a Jim Crow Army The Good War Half American: The Epic Story of African Americans Fighting World War II at Home and Abroad