Q1: Can a woman married to a Hindu AND worships at the temple inherit from her father?

No, she cannot inherit from her father.

By voluntarily participating in the religious rituals of another faith (such as idol worship or Hindu prayers) and adopting their creed, she is classified as a Murtad (apostate) in Hanafi Fiqh.

One of the absolute bars to inheritance is Ikhtilaf in deen (difference of religion). Rasool ﷺ said: A Muslim does not inherit from a non-Muslim, nor does a non-Muslim inherit from a Muslim. 

Since she has left the fold of Islam through her actions and beliefs, she is legally disqualified from inheriting from her Muslim father.

Allah Certainly Knows Best.

Q2: If a woman is married to a Hindu but does NOT worship like him or with him as he does his hindu worship, can she inherit from a Muslim?

Yes, she can inherit.

Marrying a non-Muslim that is a hindu is a severe violation of Surah Al-Baqarah (2:221) and is a major sin. However, in Hanafi Fiqh, committing a major sin does not make a person a Kafir (disbeliever).

She is regarded as a Fasiq (a sinful Muslim). Her marriage is Batil (null/void) and her relationship is Haram, but she is still a member of the Islamic faith.

Sin—no matter how grave—is not a barrier to inheritance. Only homicide, slavery, and difference of religion block a legal heir from their share.

Since she is still a Muslim (though a sinful one), she retains her full Quranic right to inherit from her father.

Allah Certainly Knows Best.