Is the recitation of the Audhu and the Basmalah obligatory at the beginning of every Surah read outside of prayer, and is the difference of opinion regarding this similar to the difference of opinion regarding it within prayer?

Seeking refuge (isti'adha) and بسم الله الرحمن الرحيم (basmalah) are prescribed only at the beginning of recitation. The basmalah is prescribed at the beginning of every surah. The issue of isti'adha and basmalah in prayer differs from that outside of prayer.