I was wondering if we can max all skills in the game or we have to choose wisely because they might have a limit?
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.
There is more than enough experience to unlock all skills relatively easily if you play your cards right - clearing all outposts undetected will take you to level 18 or so, not counting the XP from kills. Relics and lost letters also award XP, 250 and 500 points respectively; it may not seem like much, but the extra XP adds up quickly. After you reach the second island about 2/3 through the story enemies will give double XP and you will have access to Heavy Beatdown, which awards about 500 XP per 2nd island heavy.
For clearing outposts, I suggest foregoing the extra XP from takedowns and instead to rely on long-range sniper headshots - you may miss out on a hundred XP points or two that way, but you have a much better chance of clearing the outpost undetected for a massive 1500 XP bonus.
I have unlocked all the skills: it's not too hard if you are willing to spend a few hours grinding.
I did it on the south island at Charlie Camp (x238 y512). I left the area controlled by the enemy and I had unlocked the penny pincher skill. I planted land mines on the road outside Charlie Camp. You will get 120xp for each car (multiple kills). I also picked off cars with the rocket launcher. You need to loot the bodies to pay for the ammunition (I don't think you will get enough loot without penny pincher unlocked). Also you will find two cars parked in a road block north of charlie champ (both cars can be picked off with one rocket).
You should be able to get 5-10 cars which each cycle so it will take you two or three cycles to earn a skill point. It gets a bit hairy at times (if there is too much debris on the road the pirates will dismount and chase you). If things get too hot you can fast travel to Charlie Camp, restock, heal and buy more health syringes.
You can unlock all of the skills by simply playing the game, finishing it and going to capture the outposts, only one skill left for me and I finished the game, also captured all of the outposts on the upper island. And there are plenty of outposts on the lower island left.
I always selected the skill that I thought I will most need, so I started with the health and reloading guns time. If there is something I would have done differently would have been to unlock the heavy-takedown faster, after I unlock-ed it, it was 80% easier taking down those big guys from behind. I play mostly in stealth takedowns and 100m sniper shots, don't forget to first disable all alarms, if you are lucky you can shoot them from far away and the enemy wont hear you(make sure you disable the alarm or shoot all of them, shooting one wont disable the other alarms in the outpost)
Oh and btw I see Stephen saying buy health syringes, never spend money on that, just cut some green leaf like 10, and craft them rather than buying it.
TL;DR: Yes you can unlock all skills by finishing game and then liberating outposts.