I'm pretty sure the answer to my first question is no, but I still thought I'd check; I've seen a freighter pilot NPC for hire and also seen droids with pilot skill. If a PC were to hire one or buy the other, could they give them a ship and have them run between systems by themselves without the PC on board, for example to make deliveries?
If the answer is no; what exactly is the purpose of these beings? Does having them in the party simply add a skill buffer? Is the only difference between NPCs and droids that you don't have to pay droids wages?
What about the other droids? Obviously battle droids help in creature/bandit combat but most of the other ones seem kind of useless to my untrained newbie eye. Unless they simply act as skill buffers in your party?
No, NPCs cannot operate ships independently - current game mechanics don't even require pilot NPCs for any reason. Theoretically they will be required in the future, but for now ships that are squadded just mimic your ship's movements.
The pilot NPCs and majority of droids are currently functionless, with some exceptions (e.g. FA-4 Pilot droid allows you to enter docked ships without dropping out of hyper, LIN-series Miner droid assists with mining, TT-8L Sentry droids generate security events for PC/NPC movements at their deployed location).
Another important difference as I understand it is that Droids are static; they are all built to an industrial standard, and cannot develop currently past that standard. Which is to say you can't level them up; they don't get XP, and you can't boost their skill. NPCs, on the other hand, can be trained over time and ultimately will vastly outstrip a droid, with the downside being that this takes time and money in the form of wages.
Having never had the need to use droids, however, I may be mistaken on this.