My mother passed away in January 2006. My sister and I inherited her property which we sold in 2007 and split the proceeds of the sale. Are we liable for California state and/or federal taxws on that money?

There is no inheritance tax imposed by either the federal government or California, so no worries on that score. If any estate taxes were due on your mother's estate the executor would have taken care of that prior to distributing the estate assets among the heirs, so no worries there for you either.

However, you may be liable for any capital gain that you realized on the sale. Your cost basis in the property is equal to your share of the fair market value of the property as of the date of death of your mother plus your share of any capital improvements you may have made prior to the sale. If your portion of the sale proceeds is greater than your tax cost basis you have a capital gain that you must report on your income taxes. If I recall correctly the housing market in 2006 and 2007 was pretty robust, so you may indeed have a gain. But if you have a loss on the sale you cannot take the loss on your taxes (assuming the property was not rented out as income producing property).

My father passed away in June of 2011. In his will he made an amendedment allowing me to stay in the residence for up to two years. I was his care taker for about 6 years. But the last two years are where I was not allowed to leave him alone over night by himself. I was advised by the executor of the estate that there is going to be a 28 percent inheritance tax on all of the beneficiarys if the house is not sold before October of 2012. Is this correct information? Please advise.

My father passed away in june of 2011. ... Please advise.

Please don't double post questions. I've addressed your question here:
https://www.askmehelpdesk.com/taxes/inheritance-tax-california-660658.html#post3118899