I think you got your answers, but still my 2 cents 😆
1) No. This "Andha ka putra Andha" thing is not there in the original story. I don't know if it's mentioned in any of the later versions, but it was not there originally. It was creative input by BR Chopra's Mahabharat & others followed 😆 Small mercy that SP Mahabharat didn't follow completely. They showed a Maid saying that & Draupadi just trying hard not to smile. But still Duryodhan misunderstood it as Draupadi's comment so not much of a change.
2) There's a controversy regarding it. First of all Karn was not invited to participate in the swayamvar. He came as Duryodhan's sidekick. So most probably he didn't have the right to participate at all.
But I have read in discussion forums / blogs that in older versions, it is stated that Karna was not even successful in the task. He could lift the bow alright but he couldn't string it. That Dhanush's string was made from metal & he couldn't stretch it enough to tie the other end. Arjun was the only one who could lift it, string it & then complete the task. If that is the case there's no question of Draupadi rejecting him on the basis of cast. He was unsuccessful anyway. This Draupadi rejecting Karn on the basis of cast is added later to sympathise Karn.
https://mythgyaan.com/draupadi-rejects-karna/
Read this if you are interested in detailed answer 😆
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