Turbotax will not e-file a tax return that includes form 8283 if there is a signature requirement (the charity must sign the form acknowledging receipt of non-cash donations over $5000). And you can't e-file the state return unless you also e-file the federal return.
I can't tell you why the program is asking for cost basis, but it may have something to do with the optional method mentioned by the IRS (if there are optional methods, Turbotax will usually look at both to make sure which one is best for you, even if you already know which is best). Just enter the value (cost x number of shares) as of the date the previous owner died. You can look that up online.
