XP and skill points

From what I understand, skill points are added to a skill point bank. Upon reaching a certain amount in the bank, you are awarded a skill point which can be used to unlock a perk. Additionally, you are awarded XP for certain things and this is how one levels up. Skill chains can earn XP. So, XP and leveling up are mostly separate from performing skills. Is that all correct?

Also, does the amount of points needed to earn a subsequent skill point increase after earning a skill point?

You are correct and I don’t think so.