The question is
how did this movement (Vegetarianism) spread to Hinduism?
Ramayana says (Kishkinda Kanda)
पंच पंच नखा भक्ष्या ब्रह्म क्षत्रेण राघव | शल्यकः श्वाविधो गोधा शशः
कूर्मः च पंचमः || १-१७-३९
"Raghava, five kinds of five-nailed animals,
viz., a kind of wild rodent, a kind of wild-boar, a kind of lizard, a
hare and fifthly the ...
What is influence of Jainism and Buddhism in introducing Vegetarianism to Hinduism?
Vegetarianism was already a part of Hinduism, and Jainism and Buddhism are religions founded based on Hinduism.
The fact is, according to Hinduism, meat can be eaten only if the animal is sacrificed in a Vedic yajna:
5.31 - ‘The eating of meat for sacrifices’—this is ...
In Ramayana, chAranAs were mentioned in Yuddha Kanda. In this site of Ramayana, they were described as as Celestial bards.
आविवेश महान् हर्षो देवानां चारणैः सह | रावने निहते रौद्रे
सर्वलोकभयंकरे || ६-१०८-३०
When Ravana, the cruel demon and the terror of all the worlds, was
killed, a great rejoice filled the hearts of gods and chAranAs, the
Rajput are a sub-caste or order of Kshatriyas but not all kshtariyas call themselves rajput.
Kshatriyas were of three origins : suryavanshi, chandravanshi and agnivanshi (some include fourth as nagvanshi).
These are found throughout India with different names of their sub-castes.
Rajput is a predominant sub-caste of kshtariyas in North-Central India.
Siddhis (Sanskrit: सिद्धि siddhi; fulfillment, accomplishment) are spiritual, paranormal, supernatural, or otherwise magical powers, abilities, and attainments that are the products of spiritual advancement through sādhanās such as meditation and yoga.
The King in question might have obtained the siddhi - Prāpti:, ability to be anywhere at will.