Cookiesaber
"Was Spike's show-off nature developed because he's trying to feel better after being left behind?" - Probably not by intention, given his injuries messing up his memories and probably his brain, but it could totally be possible that his showing-off side is a coping mechanism
"How many people did he have to piss off before they decided to just kill him? Was it planned by higher-ups or did the other soldiers of the same ranking just decide to not help him?" - A number of people were a little peeved at being unable to control him, but it was his creator, Dr. Giovanni, who made the final call to have him killed. He took it rather personally, given that he had consider Spike/'ARMORY' to be his finest work in regards to making life.