Can you get all the perks in one skill tree? How many perks can you get for one character?

You can get a max of 80 skill perks, being that the max level is 81 according to all sources I've read. You can max out a skill tree.. a handful of them, in fact, depending on which ones you choose.

You have to travel an upward path up each skill tree to reach the top. For a perk that has two paths leading to it, you can take either path, or both. You can't, however, get that perk and then start going backwards down the path you didn't take. You always travel upward. For example, if you get to 100 Smithing for Dragon Armor by traveling the light armor side of the tree, you can't then start working your way backwards down the heavy armor side. You'd have to start from the bottom and go up.

FFFFFFFFFFFFFFUUUUUUUUUUUUUU!!!!!!!!!!!! That's what I thought I would do. Now I have to buy the whole god darned tree.....
On Topic: You have about 80+ 20 perks total. Some NPCs give perks, or so I've heard.

I've never come across an NPC that gives perks. I'm level 73 and have finished most questlines and sidequests in the game.