For question number 1 Your overall basis doesn't change as a result of a stock split but your per share basis changes. So yes, you would be able to use the historical cost of the shares adjusted for the double amount of your newly acquired shares. And now the cost of each share would be worth only half.
For question 2 you would use the fair market value at the date of inheritance (step up in basis) as the cost. As far as question number 3, you will select option B for Part 1 of the 8949 if it was short term and option E Part II of the 8949 if it was long term.
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