Learn German: Ich wollte den Akku loben, während du ihn kritisiert hast. - I wanted to praise the rechargeable battery, while you criticized it.

The conjunction während (while/whereas) simply states two contrasting actions or opinions side-by-side. The phrase dafür, dass (considering that) is used when a contrast creates surprise or violates an expectation. Since this sentence just compares my action to your action without a surprising result, während is the natural choice.

Why does the first half use the simple past ('wollte') but the second half uses the spoken past ('kritisiert hast')?

This mix is perfectly normal in everyday German! Modal verbs like wollen are almost always used in the simple past (Präteritum) because their spoken past forms can be clunky. Standard verbs like kritisieren, however, usually stick to the spoken past (Perfekt).

Could I use 'die Batterie' instead of 'den Akku' here?

It depends on the device. der Akku (short for der Akkumulator) specifically refers to a rechargeable battery, like those in smartphones, laptops, or electric cars. die Batterie usually refers to a single-use, disposable battery, though Germans sometimes use it broadly.

Why is the pronoun 'ihn' used in the second clause?