1. Lies, since the symbol of the Mysore Kingdom was the Gandaberunda, the two headed bird. Varaha was the symbol of the Vijaynagar empire which was destroyed more than century ago.
2. Tipus astrologers predicted that he could become an emperor if he performed some rituals. So he did, in Sree Ranganatha Swami Temple and made that donation.
3. The Hindu priest Srikanteshwara swamy of the famous temple in Nanjangud, in Mysuru district was also a noted ayurvedic expert. He was also a physician to Tipu. Tipu called him “Hakim Nanjunda".
Tipu Sultan’s royal elephant which suffered from eye problems had lost its eye sight. Tipu was told about the glory of Srikanteshwara at Nanjangud temple that one’s wishes would be fulfilled if one offered prayers to the lord with all devotion. He was advised by the priests of the temple, to bathe the elephant in River Kapila and wipe its eyes with the river water used for the abhishekam of Lord Srikanteshwara for one mandala that is 48 days. To his surprise, the elephant regained its sight.
That is how he donated that shiv ling.
4. Tipu was a VERY superstitious man. He always conducted religious rituals and wore apotropaic objects and trinkets—Hindu as well as Islamic—either to avert a disaster or to attain success in his undertakings. He placed great emphasis on his dreams and has a book written that details his dreams.
Tipu even sported a gold ring etched with the name of the Hindu God Rama—a gift from the Guru of the Sringeri Math. But he had no qualms about destroying the Harihareswara temple at Harihar, the Varahaswami temple at Srirangapatnam, and the Odakaraya temple at Hospet.
Tipu Sultan’s ceremonial sword bears an unabashed admission inscribed on it:
“My victorious sabre is lightning for the destruction of the unbelievers.”
But at the same time, before his final war with the british, He ordered for all the ceremonies prescribed by the Brahmins to be duly performed, and having given them presents, requested their prayers for the prosperity of his government. He also ordered to be slaughtered two elephants with all their golden trappings, and he then had large sums of gold mohurs distributed among the beggars.
His hate for non musilms was such that he even threw out Ahmadeias from his kingdom.