1. Does any one of the non-Muslim mother or father have rights over their child born out of wedlock? Same for the siblings of this child from these parents?
Parents have rights upon their children irrespective of whether they were born to them legitimately or not. Almighty God says in the Holy Quran [29:8]: “We have enjoined man to be good to his parents. But if they urge you to ascribe to Me as partner that of which you have no knowledge, then do not obey them.” He also says [31:14]: “We have enjoined man concerning his parents: His mother carried him through weakness upon weakness, and his weaning takes two years. Give thanks to Me and to your parents. To Me is the return.” As such, one must express kindness to their parents and fulfill their needs, and if they are not guided to the right path, the child should try to guide them. The same goes for siblings.