1. Spellings are correct.
2. I think it is grammatically incorrect. It uses the verb, "hona" (to be) so "beti hona" means, "to be a daughter" (so the sentence means, not afraid of being a daughter). The correct words should be, "beti peda hone se dar nahi lagta" بیٹی پیدا ہونے سے ڈر نہیں لگتا (not afraid of a daughter being born), or a better alternative is "beti ki pedaish se dar nahin lagta" بیٹی کی پیدائش سے ڈر نہیں لگتا (not afraid of the birth of a daughter).
In Punabi language we usually say, "beta hua he/beti hui he": "baby boy is born/baby girl is born" (the verb "born" is left out). We cannot do the same in Urdu.
The second part of the sentence uses plural rather than singular. It should also be singular as in the first part. So instead of
بیٹیوں کے نصیب سے (ڈر) لگتا ہے
it should be
بیٹی کے نصیب سے (ڈر) لگتا ہے۔
Or the first part should also use plural for the sake of consistency.
"Beti kay honay sai dar nahin lagta, betiyoon kay naseeb sai lagta hai ''
"Beti kay honay sai dar nahin lagta, betiyoon kay naseeb sai dar lagta hai