Anybody who submits to the religion of Islam with the two testimonies is a Muslim, provided there is no animosity against any of the Imams (peace be upon them). Iman depends on believing in the Wilayah of the Ahlulbait (peace be upon them).
Human nature necessitates differences in opinions in every field, including Islamic jurisprudence, since it is one of the sciences that depend on in-depth and detailed derivations, like other sciences. So, it is natural for scientists to arrive at different conclusions as long as they are thinking freely and objectively. As such, the Shia school of jurisprudence has developed as a result of the intellectual efforts of many great scholars throughout centuries, may Almighty Allah shower His blessings over their souls and guard those still amongst us, for their preservation of the religion from external influences and powers and maintained the religion in its pure and untainted form.
Kaffara is not obligatory in the said case.
Yes, it is permissible, but it is better if the payment is given and taken as a gift.