You're correct.
And no, you cannot send the absorbed chakra into your body, at least not with our current techniques. I believe you would be exposed to the effects of Senjutsu and get petrified, yes.
Enter, Inhaling Maw. Meet the essential Meiton technique that a lot of other techniques are based on its effect.
(Meiton: Kyūketsukō) - Dark Release: Inhaling Maw
Rank: B
Type: Offensive, Defensive
Range: Short
Chakra cost: 20
Damage points: N/A
Description: The user uses their dark release to forcibly extract the physical and spiritual energy (chakra) of another ninja and absorb it through the upper square of the mark on his left hand, which can then be used to perform Dark Release: Judgment.
Note: Can absorb up to A-Rank Wind, Fire and Lightning techniques, S-Rank raw chakra or C-Rank Water, all within reason. Has no effect on Earth techniques.
It's a simple concept where you use either of your dark mark and absorb an incoming technique. Inhaling Maw is an exception because it does not follow the usual S/W scheme of Dark Release, but it can only absorb what is stated in the note. So, perform this technique against an incoming one, which I'm gonna demonstrate.
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Feitan stands in front of his opponent as he gathers lightning chakra in his palm. With a flick of his wrist, a compressed lightning ball is flung with great speed toward the student, intending to hit him in the stomach. "Show me your dark spirit!"
(Raiton: Sanda Appu) – Lightning Release: Thunder Up
Type: Offensive
Rank: A
Range: Short-Mid
Chakra: 30
Damage: 60
Description: The user concentrates a lot of lightning chakra into their hand, compressing it into a ball of lightning energy. The user can then hurl it at the enemy or trust it forward in a melee attack. Once the ball hits the target, it expands into a massive lightning explosion.