a)
Take Heart This skill allows Kakuzu to rip off hearts from enemy characters. Kakuzu will successfully gather a heart if an enemy will have less that 10% hp level (percentage count rises with improving that skill). By killing off an enemy character in such a way, Kakuzu is able to store up "1 life" per each kill thus allowing him to come back to life should he die. The number of hearts cannot exceed a limit of 5.
This skill is the most important skill Kakuzu has so it must be leveled up at least once and each time you kill an enemy your main goal would be taking the heart. Later in the game it will be difficult for your enemies to kill you on the line with several hearts at your disposal so be careful on both duel arena and on the lines. If the enemy is too close to your tower, make sure you are ready to use your "Hands Grip" skill along with Douton if necessary to slow down an enemy and deal maximum damage in order to lower down his hp level to the minimum and eventually use the "heart" skill
b) Douton Defence/Attack combo
This skill allows Kakuzu to strengthen his body with the earth element improving Kakuzu's defence as well as allowing him to channel this power into one attack(however if you choose to attack, you will lose the defence buff immediately after you cast the spell and the time to use the spell is quite short)
The skill itself is quite useful in the beginning, for it helps a lot when farming mobs from gold due to its short cool down and slows down the enemies as well as stuns them a little (which is quite to your advantage if an enemy hero is right next to your tower). However my advice to level it up only once or twice in the beginning
c) Hand's Grip
A very useful "hold" skill which Kakuzu has. This skill both holds and deals damage to the enemy. There is a chance that upon the use of this skill, Kakuzu can catch several targets at once which is quite useful especially on duels.
This skill is highly helpful and should be leveled up at all times!In the worst case scenario, it might be a good idea to level up this skill to the maximum at the beginning.
d)Heart Monsters
This skill allows Kakuzu to unleash the hearts of his victims and put them inside the black monsters. The more hearts Kakuzu has, the more demons will spawn. As i already have mentioned earlier, there is a limit of 5 hears Kakuzu can have in total. If you level up this skill to level 4, those hearts will be able to use some of the very powerful jutsus Kakuzu has. Fire element: A huge field of fire which builds up in about 1.0-1.5 seconds and spreads out in several directions. Along with this skill, the fire monster is capable to deal extra damage when attacking physically; Wind element: Black monster blows out a huge tornado towards a certain direction dealing damage and pulling everyone in a line (including Kakuzu and allies if they will get in a way). Along with the active skill, this air monster has a passive ability which allows him to deal double damage in normal physical attack. And lighting: two big lightning bolts coming from the black monster dealing a very high damage in a line. Also a passive ability is in tact which helps slow down the enemy. There is also another heart which is useless in some way or another. It has a water passive skill which gives a chance upon a physical attack to deal some extra damage creating a water wave.
In the beginning it is worthwhile to level up this skill at least once, however if you see that you are getting new hearts really quick, then start leveling up this skill as soon as possible for it is crucial that Kakuzu gets those active skills from the monster as soon as possible, be it even one only its still good enough to kill. Also on skill's levels 1 2 3 and 4 there is a limit on your heart's duration. If it happens that you didn't have enough mana to call them back into your body(by activating your ult-Heart Transformation) those hearts will die permanently, so be aware of that. Also if you will acheive lvl 4 with that skill, be careful not to lose the monster. If the monster will die Kakuzu will lose one heart.
e) Heart Transformation
This is your greatest and strongest skill of all. By having at least one heart, Kakuzu is able to transform with it into some sort of black demon. While in this form, Kakuzu's hp and damage are boosted highly and should be used quickly before the duration of the skill runs out. While being in this form Kakuzu acquires a new skill which allows him to blow wind and fire from the front.
This is a useful skill however not of a high priority. Should be leveled up at least ones in the beginning for the sake of first duel. Don't hurry up using the Fuuton+ Katon combination. My advice is to use it only when enemies surround you or you pull someone towards the wall/tree and this will help you channel this power in exactly the same way as Sasuke's Nagashi.