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Question 1 - Yes, the sale of one-half of the duplex to son should have triggered depreciation recapture for one-half of the property.  For California taxes, the depreciation period for residential rental property is 45 years. So that requires a separate set of calculations.

Question 2 - Yes, it appears there was a long-term capital gain on the sale to son of one-half of the property.  However, California taxes long and short term capital gains as regular income.  No special rate for long term capital gains exists. 

Question 3 - If the son was actually paying the mortgage interest and property tax, then the son can take the deduction for those items. 

Question 4 - Yes, because mother was collecting rent, the mother should report that rental income on the return for the year in which the rental income was collected.

Question 5 - Yes, it appears that the cost of the property was completely recovered and thus, there is no further depreciation to claim at least on the federal return.

Question 6 - Perhaps, if no exception applies.  You do not have to withhold tax if the CA real property is:

• $100,000 or less
• In foreclosure
• Seller is a bank acting as a trustee
• See Form 593, Part III for a complete list of full exemptions, and Part IV for full or partial exemptions.

Question 6(1) - Yes, it is the value of the property on the mother's date of death.  But there is the option to use the FMV of the property on the alternate valuation date, but only if the executor of the estate files an estate tax return (Form 706) and elects to use the alternate valuation on that return. See the Instructions for Form 706.

Question 6(2) - the son's depreciation would begin on the day the property is placed in service.  On the federal side, the cost basis to use for depreciation purposes is the lesser of (1) the fair market value of the property or (2) the owner's adjusted cost basis.  

@Trusteeof3