I noticed that there haven't been any replies, so I e-mailed a friend of mine who was involved in Penn Station operations for a number of years, and this is what he came up with:
"In question 1 [about the tail track] you are describing the 'Kelly track.' It's apparently named after an engineer named Kelly who derailed either a yard engine or a yard move on that track. Among other things, it was also used as a penalty box. If the stationmaster was mad at a yard crew, he'd send them up to the Kelly track and let them sit there all night. It was apparently used as a 'for-now' track and somehow played into switching moves. [this next bit refers to a comment of mine about whether there was a station shifter ('switcher' on non-Standard railroads) and whether there was anything for a station shifter to do if plans were for everything to move to and from Sunnyside] Remember, no through train from New England ever got through Penn Station looking the way it did when it arrived. And Post Office cars were added to equipment that started in Sunnyside."
"I don't know about the narrow platform adjacent to Track 17. At one time, it was always used for LVRR trains."
He's going to ask around among some other people, and if he comes up with something more, I'll post again.