Indeed. However you get way more skill points at the beginning than you would get for a long time levelling up. THis is one of the ways that the inbalance between older players and new ones is fixed. Older players could have higher/more skills but a new player will not be at a serious disadvantage if they set themselves up correctly.
As for HP, yes, but not that much. I think you have to reach maybe lvl 5 before you starting HP is doubled, but not sure on that. In SWC levelling is more of a way to fine tune your character rather than most other games where you continually get exponentially more powerful with each new level.