Hinduism ~ Can Geeta be taken as a spiritual authority.....?

Yes. Its dhyanasloka/meditative chant says that it is the essence of Vedas and Upanishads, the most authoritative spiritual texts. Gita is known as the Cow of Vedas/Upanishads ( vedOpanishadO gAvO ).It contains the essence of six systems of philosophy/darshanas - nyaya, vaishesika, sankhya, yoga, mimamsa and vedanta. It contains all the "methods' of spiritual practice - jnana, bhakti, karma, raja. Gita is truly a guide to life in general, spirituality in particular.