I will try to provide reasonable answers for your questions

1. Multiple Paroles
1a) Paroled below Port Hudson, at Prophet's Island, May 5th, 1863. Sent to New Orleans, La., to be exchanged.
1b) Roll for July and Aug., 1863, Absent. Paroled Prisoner April 17th, 1863.
1c) Paroled at Washington, La., June 16th, 1865, Res. New Orleans, La

Probable answers:
1a) After being captured at Franklin on April 14, 1863, Sgt Campbell was a POW and was carried by US boats to the Prophet's island area on the Mississippi River. On April 17, 3 days later, he was released by the Union Army on parole and could not participate in fighting again until exchanged.
1b) On being paroled, soldiers returned to their side, but were kept out of line units until formally and legally exchanged. Sgt Marsden may have been at a Confed camp away from the front or he may have been sent home with documents to explain his absence if stopped by Union or Confederate patrols. The Roll for July and August 1863 indicates that he was away from his unit on parole from the April 17, 1863 Union release. This is the same parole mentioned in answer 1a. The US commanders released he and others so they did not have to guard or feed them.
1c) Immediately after the end of the war in LA (late May and early June of 1865) all former LA Confederate soldiers had to report to a Union command post near their home or place of residence and to sign a final parole for the war, promising not to take up arms against the US again for the Confederate cause. Marsden Campbell complied and signed his final parole on June 16, 1865 at a Union Command Post in Washington, LA.

2. Possible demotion.

Probable answer:
2) Marsden's CSR shows that he was a Private at the end of the war. If you look at the NPS-CWSS site, it shows that he went in a Sgt and ended the war as a Private. The 1st card in his NARA-CSR M320 file indicates he went into (1862) the 2ndLC as 1st Sgt, and out (1865) as Pvt. I have not seen the document you mention, although I have spent time at the Tulane Archives. The Special Order indicates that he was placed under close arrest in April 1865, but you would have to locate the follow-up documents to determine the reason and outcome. These documents may or may not exist, but I would think that the Jackson Barracks Archives or the Brent papers at Tulane are the best places to look.

As Steve indicated, many soldiers were placed in detention or arrest for many things. In most cases they were trivial events that passed, or misunderstandings on a part of an officer - a "you were ordered to, but didn't" kind of scenario. As an example, Lt John Sibley of Co E 2nd LA Cavalry was placed under arrest in late 1864 by a Texas Major for some misunderstanding and was then released and restored to duty by Col WG Vincent. Col Vincent or Capt Furman had told Sibley to do one thing and the Texas Major thought he had been ordered to do a different thing. In the end, all was well and service was completely honorable. This is the likely scenario for Marsden, although it may simply be that the end of the War was so close that his charges were not adjudicated or resolved before the end of May.

I strongly suspect that Marsden Campbell's service in the 2nd LC began and ended honorably.

Hope this helps

Don Parker