Yes to question 1. You need to file a California non-resident return to report the sale of the inherited house. Question 2 is confusing to me though when you mention "shows a refund of about 66% of the original 3.3% that was pulled out at the sale".
To determine the capital gains on the house and if this house was never your personal residence, you would use the Fair Market Value (FMV) at the time of the decedents death. Then you would compare the sale of the house with the FMV by substracting the FMV from the proceeds. If the result is positive, you will pay capital gains on the gain. If negative, you will not pay capital gains but you cannot declare a capital loss either.
Normally, if the death is recent, the FMV and proceeds are nearly identical and the capital gains are minimal at best. You also mention a $250,000. Normally, this dollar amount is only considered if you are reporting capital gains on a personal residence if you own and have lived in your home for two of the last five years.
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