Packet data is all your data whether it's HPSA+ or LTE, edge, etc... If it's unchecked, all your data is off. You'll still have cellular service for phone calls and SMS, but no data.
I'm not exactly sure what the background data thing is exactly, but it's not the same as having apps sync in the background which is the next option listed. I would leave it on.
For some reason, SMS does the whole mini video thing with the "play" icon on the thumbnail. Coming from an iPhone myself, I don't get it either, but they still send and receive like SMS I believe.