What NPCs can you permanently kill in Bloodborne, and what are the implications

The summoning range has since been updated via patches. As of patch 1.05, research found here indicates the following rules:

Let x be your level.

For upper limit of level you can summon:

x + 20% + 20

For lower limit of level you can summon:

x - 20% - 20

For upper limit of level you can be invaded by:

x + 10% + 10

For lower limit of level you can be invaded by:

x - 20% - 20

It should also be noted that if you are using passwords to summon a friend, this limit will be ignored and you can summon them regardless of their level. Players who are significantly higher than the summoner who are summoned this way will have their levels scaled down.

Here is a nifty calculator which does the math for you!

Primarily you're right in that they're meant to just be additional healing items, generally with special qualities compared to your regular blood vials (heal-over-time, increased healing amount, temporary buff to stamina recovery). There's an interaction between a couple of NPCs depending on which special blood vials you decide to take:

If you've rescued both Adella and Arianna (via Oedon Chapel, not Iosefka's Clinic), you can get special blood vials from one or both of them. Receiving blood from Arianna three or more times causes Adella to become jealous, and she'll kill Arianna the next time you load into the Cathedral Ward lamp area. This has later implications for the storyline, with the general consensus being to try and keep Arianna alive.