I've played the game and looked through the wiki, there is no use that I've seen for the miscellaneous items that you gather from loot chests and dead bodies. The names for everything is just filler, make the player feel a sense of pride when he picks up a Diamond or Smartphone. The only quest items you will gather would be herbs and leather, occasionally some other item that you can only get while performing the quest.
Here are the quotes:
"In another moment down went Alice after it, never once considering how
in the world she was to get out again."
"'I like the Walrus best,' said Alice: 'because you see he was a LITTLE
sorry for the poor oysters.'
'He ate more than the Carpenter, though,' said Tweedledee."
"'Oh, you can't help that,' said the Cat: 'we're all mad here. I'm mad.
You're mad.'
'How do you know I'm mad?' said Alice.
'You must be,' said the Cat, 'or you wouldn't have come here.'"
"'Have you guessed the riddle yet?' the Hatter said, turning to Alice
again.
'No, I give it up,' Alice replied: 'what's the answer?'
'I haven't the slightest idea,' said the Hatter."
"'What do you mean by that?' said the Caterpillar sternly. 'Explain
yourself!'
'I can't explain MYSELF, I'm afraid, sir' said Alice, 'because I'm not
myself, you see.'
'I don't see,' said the Caterpillar."
"'Everything's got a moral, if only
you can find it.'"
In the "If only you can find it" part, the words "kill", "fuck" and "find" are shown alternately until settling at "find" in the end.
The screen captures are from this Youtube video:
I got the text from Project Gutenberg:
Alice's Adventures in Wonderland by Lewis Carroll
Through the Looking-Glass by Lewis Carroll
All quotes are originally from Alice's Adventures in Wonderland, except the second quote ("I like the Walrus best.."), which is from Through the Looking-Glass, and What Alice Found There.
Best Answer
Fully Inked is an achievement that requires you to "Earn every tattoo by learning all the skills". This confirms that it is possible to earn all skills and since there is no new game + mode, it must be possible to earn on a single playthrough.
It is unlikely that all story and side missions combined would provide enough XP to unlock all skills however given the enormous amount of enemies populating the game world, it is very likely that you could pick up any remaining skill points by grinding enemies.
As other posters have mentioned, enemies respawn in the areas around an enemy-controlled outpost (red bubbles on your map). You could clear these areas multiple times (as long as you don't actually capture the outpost) OR you could maximize the amount of XP earned from each enemy you encounter by performing headshots (2.5x XP) or special melee takedowns (3x - 7.5x XP).
If you are set on unlocking all 24 skills as soon as possible I would make unlocking the Death From Above and Death From Below skills a priority. These skills allow you to perform melee takedowns from above or below an enemy for a 5x XP bonus. There are also upgraded 'Dual' versions of each of these skills which allow you to subdue 2 enemies at once (7.5x XP). Getting these skills early and using the takedowns often could significantly shorten the amount of enemies required to earn all skill points necessary.