I am going to do this one off the top of my ehad, always a dangerous practice, so please excuse any inadvertent errors that may creep in.
My primary knowledge of the Palmetto Sharpshooters comes during the time while the Hampton Legion was brigaded with the PSS from November 1862 until March 1864, but I am at least passingly familiar with their operations in some of the other fights. At 2nd Manassas Jenkins Brigade, in Pickett's Divison (temporarily under James Kemper), came into action on the right of and in support of Hood's dvision, supposedly in echelon, but the advance by Kepmer's Dvision appears to have been in division line. They of coruse would have been preceeded by skirmishers. The PSS was one of the regiments in the line of battle, not posted in front.
At Sharpsburg Jenkins Brigade (he was absent due to wounds received at 2 Manassas) was in what passed for a queit sector of the Confederate line, but given the nature of the fighting there, there weren't any truly quiet sectors. Toombs Brigade had suffered heavily at 2 Manassas (under Benning), and was posted on the Confeederate right, overlooking the Lower Bridge that has come to be forever known as Burtnside's Bridge. Essentially, Toombs' decimated little brigade was facing the entire Federal IX Corps. The upshot of it was that Longstreet, who was in charge of the Confederate right, funnelled whatever reindforcements he could spare from his line (which was under heavy pressure). My recollection is that Jenkins' Birgade was next in line to Toombs.
I am not familiar as to how the brigade was placed in line, but if the PSS were on Jenkins' right, they would have been the natural choice to send over reinforcements to Toombs. There is, incidenmtally, an excellent little book, written ca 10-12 years ago, which deals with the dfeense of the ridge above the Lowere Bridge. it focuses on Toombs Brigade, but gives an acocunt of the South Carolinains' presence. I found a copy at the Robert Toombs House in Washington, Georgia, and my copy is somewhere in my library.
After Sharpsburg, Jenkins' Brigade was not seriously engaged for more than 13 months. At Fredericksburg the PSS were one of the reigments in Jenkins' line of battle,. not occupying an advanced position. In desultory skirmishing along the Balckwater in alte March and early April 1863, the PSS were posted at Franklin, and held the line of the river, although they, in connection with other regimetns of the brigade, sent pickets and scouts across the river toward the Nansemond. Duyring the siege of Suffolk, Jenkins' Brigade was on the right of the Cofnederate line, in a quiet sector (as indeed the whole front was), and took theri normal ortation in the rifle pits. The total birgade losses in this three week operation operation were less than 30.
Jenkisn' Brigade missed Chancellorsville, Gettysburg, and Chickamauga. During the siege operations against Rosecrans in Chattanooga, Hood's Division occupied the Confederate left. Jenkins Brigade hedl a line along Chattanooga Creek, near the foot of Lookout Mountain. From everything I can come up with, each of the regiments of the brigade sent out two ro three companeis on picket each day -- the time of relief was noramlly 11 P.M. Wen it came time for Jenkins -- who was in acting divisional command of Hood's dvision -- to assign sharpshooters to picket the south bank of the Tennessee and harrass Federal trains across the river, he assigned men from Robertson's Texas Brigade to that task (and they very effectively shut down the wagon road on the north bank, casuing a long detour, and forcing the Federals to the brink of starvation -- by the end of October the Federals were on quarter rations, and horses and mules in the city were dying at the rdte of as many as 200 a day.)
When Jenkins' poor generalship and Longstreet's outright disobediaence of Bragg's direct orders led to Hooker openign the route from Bridgeport to Brown's Ferry on October 27-28, Longstreet belatedly sent Jenkins into Lookout Valley, but with only four of his five brigades, for a night attack. Bratton, commanding the S.C. brigade, advanced up the Valley in line abreast, each regiment preceded by its own regimental skirmishers. During the night engagement at Wauhatchie, Bratton deployed his reigments in line of battle, fonforming to the horseshoe shape of the Federal line.
In the advance upon Knoxville, Bratton's brigade held the advance from the crossing of the Tennessee at Hough's Ferry through Campbell's Station. But the brigade skirmisheres apepar to have come from each of the regiments, and were under the command of LCOL Thomas M. Logan, of the Legion, who had developed into an outstanding picket and skirmish officer; Robert E. Lee called Logan the "best outpost officer" in the Army of Nrothern Virginia, pretty high praise.
I am not familiar with the operaitons of Bratton's Brigade form The Wilderness through Cold Harbor, or while it was engaged south of the James before Petersburg. The Legion had been mounted in the spring of 1864, and I simply have not follwoed the S.C. brigade during the spring of 1864. But beginning in July 1864, all or parts of Bratton's brigade were sent north of the James, and frequently fought alongside or near Gary's Cavalry Brigade, to which the now-mounted Legion belonged. The fighting of Bratton at Fussell's Mill in August was a stand-up fight, with Bratton occupying the trenches overlooking the crsosing of Bailey's Creek. At Fort Harrison on September 30, and at First Darbytown on October 7, Bratton's bvriogade mnade failed charged on fixed Union entrenchments, attacing in line of battle. In both engagement Bratton attack in line abreast, in compliance with orders. At Secodn Darbytown on October 13 and at Willaimsburg Road on October 27, Field deftly handled his divison, mvoing troops raidily along the line in time to occupy the trenches and turn back repeated Federal assualts.
The bottom line is that as far as I know, the PSS were deployed in the same manner as the other infantry regiments in Jenkins'/Bratton's Brigade. Certainly some of the men were undoubtedly better at picketing and skirmishing than others, but the noraml practice was to roitate this duty, which was onerous and dangerous. To have permanently assinged men to picket or skirmishing would have caused a mutiny.
On the other hand, there were alsways a few daredevils in every unit who volujnteered to be scouts. Those were the guys who snuck in and out of Federal lines. The Texans were renowned for their ability as scouts in the Army. But every unit has a handful of thses men, and of cours,e so did the Federa units as well.
Please understand that I do not in any way cast off on the quality of the men who served in the PSS. It was a regiment which was ably officered throughout the war. But from what I can tell, it was deployed by its brigade commandrrs in the same manner as the other regiments in the brigade.