Mother and Son own duplex occupied by Son

1) Mother bought duplex in California in 1980 for let's say, $100k, and made capital improvements of $50k.
2) Mother rented out both sides of said duplex.
3) Son moved into one side of the duplex along the way and paid rent.
4) Mother sold half interest to Son in 2017 for $417k. Son continued to live in one side; renters occupied the other. Son financed the sale with a mortgage. Son paid the mortgage and property taxes. Mother collected some rent, with the agreement that she would report all of the rent as income. Son deducts all mortgage interest (only his name is on the 1098) and all property tax.
5) Mother dies in 2021. 100% of property passes to Son as "Joint Tenant with Right of Survivorship." Let's say the FMV at death was $900k.

Questions for Mother's back taxes that were never filed:
1) Must Mother recapture depreciation of 50% of purchase price plus capital improvements (since it was more than 27.5 years) on her 2017 return? So 50% of $150k is $75k, times 25% recapture tax would be $18.75k?
2) Must Mother pay capital gains on $417k - $150k/2 = $417k - $75k = $342k on her 2017 return?
3) Was Son allowed to deduct all mortgage interest and property tax?
4) Is Mother allowed to report all rental income since sale in 2017?
5) Depreciation: after sale to Son in 2017, I understand that there is no further depreciation for Mother or Son since rental "side" was fully depreciated. Correct?
6) Should Mother or Son have paid the California Franchise Tax of 3 1/3% of $417k?

After Mother's death:
1) Is half of FMV at death stepped-up for Son? So his new basis for capital gains when he sells is half of the FMV at death ($450k), plus his purchase price of $417k = $867k?
2) Does Son's depreciation begin all over again at that same basis?

Thank you for your time. As you can imagine, it is difficult to google this exact scenario.