I have read about what happens exactly during a prana prathista ritual. I understand that certain procedure is followed for instilling prana in an idol. But I want to know if the idol does have any soul and cosmic consciousness.
Swami Sivananda in "All About Hinduism" Page 115-119 writes
Idol or Murthy (Vigraha), Sun, Fire, Water, Ganga, Saligram, Linga are all symbols or Prateekas of God which help the aspirants to attain one-pointedness of mind and purity of heart. A symbol is absolutely indispensable for fixing the mind. For a Bhakta or a sage, there is no such thing as Jada or insentient matter. Everything is Vasudeva or Chaitanya-vasudevah sarvam iti. The devotee beholds actually the Lord in the idol. Narsi Mehta was put to test by a Raja. The Raja said: "O Narsi, if you are a sincere devotee of Lord Krishna, if as you say the idol is Lord Krishna Himself, let this idol move." According to the prayer of Narsi Mehta, the idol moved. The sacred Bull Nandi before Siva's idol took the food offered by Tulasidas. The Murti played with Mira Bai. It was full of life and Chaitanya for her. When Appayya Dikshitar went to the Tirupati temple in South India, the Vaishnavas refused him admission. The next morning they found the Vishnu Murti in the temple changed into Siva Murti. The Mahant was much astonished and startled, asked pardon and prayed to Appayya Dikshitar to change the Murti again into Vishnu Murti. Kanaka Dasa was a great devotee of Lord Krishna in Udipi, in the district of South Kanara, in South India. He was not allowed to enter the temple on account of his low birth. Lord Krishna turned round to enable Kanaka Dasa to get His Darsana.
The Murti is the same as the Lord, for it is the vehicle of the expression of the Mantra-Chaitanya which is the Devata. The same attitude should the devotee have in regard to the Murti in the temple, which he would evince if the Lord would appear before him in person and speak to him in articulate sound.
Chaitanya Charitamrita a great Vaishnava text says
The maha-bhagavata, the advanced devotee, certainly sees everything mobile and immobile, but he does not exactly see their forms. Rather, everywhere he immediately sees manifest the form of the Supreme Lord.(CC Madhya 8.274)
Since the Murthi is Supreme Lord itself and that Lord assumes various forms as per devotee's request (Vide Gita 7.21) we can conclude that Murthis have cosmic consciousness and they can talk speak or move when pure devotees request so.