I don't really understand how these perk points work. I've noticed some that give you points don't add to the total amount of points you have, while others do.

For instance, I believe the first perk you get is Learn the Ropes, which is 10 points. But when you get it, at the bottom your points show up as 0/10. Then some other perks that give you points, will add to the total. I think the perk Appreciated does, which you get when you hit lvl 5, and it's worth 25 points. Then it shows up as 25/35.

Why is it some of these perks add to your pool of points, while others don't, but they are still worth points? I'm not understanding.

It seems you can spend them at special vendors in the main city.

You can't use all your perk points, you will only be able to access X amount of perk points at any given time. You buy perks in Millenium City. It's not that it doesn't give you the points, it does give you the points it's just that you will not have access to it till a later time (possibly higher level and up).