Nathan Carsch - Parents of Nathan

But:
if Eva was born 4.3.1843,
Nathan couldn't have been born on 24.3.1843.

Hmm!?

Gerson & Frederika must definitely be the parents as they marry in 1836.
Whereas Simon & Sara Carsch don't actually marry until 2/7/1843.

One possibility is that Eva's birthday is a typo, and that she too was born on 3/24/1843 (not 3/4/1843) which would make them twins?

"24th" prescribed to "4th" - that was my guess too.