yes Fatimus you are right in summarizing the origin of SE.
first of all, SE was scarred following a chopper crash in 'Nam while fleeing from VCs..SE suffered from severe face burns and that's how the iconic facemask comes in...the scars that developed from the crash and several surgeries that followed had almost disfigured him...he did wore a human mask complete with hair but ever since the crash,he lost his ability to speak.
SS recognized the fighting potential of SE and hence urged him to join his clan .He only did so upon returning to the States after the accident that left him scarred. And the main motivation for joining was him receiving the tragic news of the death of his parents and sister in a car accident.
AS for the death of Hard Master ,it was during the period that both SS and SE trained..FF was hired by CC to kill SE (CC's brother was involved in the accident that killed SE's family) and blames SE for it.
FF infiltrated Arashikage clan but upon witnessing the skills of SE,he knew he was no match...he then recommended Zartan for the job.
Zartan accidently killed Hard Master whom he mistaken for SE and he did this using SS's arrows.hence SS was blamed for Hard Master's death and he ran away from the clan but it was bcoz he was chasing after his uncle's killer.however in his mind ,SS blamed SE for his uncle's death.
SS was later recruited by CC as his right hand man ,performing deeds that CC entrusted to him .he clashed with the Joes on several occasion but later found out that it was Zartan who killed his uncle,under orders from CC and FF.
from there,SS joined the Joes but later was captured and was subjected to numerous brainwashing sessions courtesy of Dr. Mindbender's brainwashing machine..the reason for this is to maintain SS's loyalty to Cobra and specifically, CC.
SS did broke free from his brainwashed state by performind Arashikage's methods on meditation..even SE helped him during one of the issues of MArvel Comics where the entire Ninja Force was brainwashed by FF..
you have to read the comics for more details.