Does the philosophy of advaita i.e non-dualism provide the theological ground for Kriya Yoga? If yes, then why does Paramhansa Yogananda address God in a dualistic manner in almost all of his writings?
Thank you for your inquiry: it is an important and subtle question. Yes, the Self-realization teachings espoused by the line of Kriya Yoga masters (from Babaji to Yoganandaji) are deeply rooted in Vedanta: in advaita (non-duality).
However, even Krishna admits in the Bhagavad Gita that, for embodied beings, worship of the Absolute is arduous; the I-Thou relationship is more effective so long as one is still identified with the body and ego. Krishna also espouses the practice of yoga (meditation): contemplation of God in one form or another. So also does Patanjali in the Yoga Sutras. Yet no one would doubt that both the Gita and the Sutras are aspiring to Oneness in God.
Devotion and selfless service, together with following the guru’s instructions regarding pranayam/meditation: these are the safer path to the Absolute. Like Ramakrishna Paramhansa (for whom his guru, Totapuri, had to push him to go beyond the I-Thou relationship with Goddess Kali), there are many stages and steppingstones for the soul’s evolution — like a caterpillar becoming a butterfly.
Devotion is sweet, however. And, so long as in human form, many saints and realized masters prefer the lila (divine play) of love for God in a form held dear.
Blessings and joy to you!