from what i know, every skill level up contributes to a character level up, and because skill level maximum is (100?), once a player reaches 100 on every skill they can no longer level up their character level and thus no longer choose anymore perks; max level will be less than number of perks-however many perks there are im not sure
There are 280 perks to choose from and it is my understanding that you stop receiving new perks at level 50; however, you can continue to level up from 51 until the mathematical maximum level which is around level 70-80.
I haven't seen the interview where Todd specifically mentions no more perks after level 50, perhaps someone can provide a link. I know that he has said several times that the game is designed to be a "level 50" game compared to a "level 20" game like FO3, in the sense that most people will not exceed level 50 when playing Skyrim for a really long time.
Perks get unlocked in between character levels when you increase your skill to the minimum amount for the specific perk. Then when you level up the character you get to choose one of the unlocked perks.
Todd Howard: Perks “come from levelling up character rather than skills. Pick a perk when you level. It’s like a standard skill tree but they have requirements, not just the one below it. You see a perk you like and say I’m going to start using my sword more because I want that perk.”http://www.rockpapershotgun.com/2011/04/18/skyrim-skills/
In other words, some perk unlock requirements are simply "the one below it" in the chain.
Other perk requirements are skill must be at X or higher - you have to increase a skill (like 1H) to a certain level in order to unlock some of the perks.
And most likely there are some perks that have both kinds of requirements in order to become unlocked.