There is no "Basic" edition when using the TurboTax online editions. If you are referring the Free online edition, then no it will not handle investment sales with a gain or loss. You will need to upgrade to the Premier online editions for what you need to report on a federal tax return - https://turbotax.intuit.com/personal-taxes/online/
There is a Basic edition in the TurboTax desktop CD/Download editions which can handle your needs. But it does not include a state tax return program. That would be an additional charge of $40 to download a state program. Or you could use the Deluxe desktop editions which will handle your needs and does include one state program download in the purchase price - https://turbotax.intuit.com/personal-taxes/cd-download/
No, the basic edition doesn't include Schedule B - Interest and Dividend Income, Schedule D - Capital Gains and Losses, etc. You'll need to have at least the online version of the Premier edition. You could use the Deluxe edition of the CD/Download product.
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All versions of the CD/download version of TurboTax support all forms. TurboTax Basic is only available in the CD/download version, not online. TurboTax Basic can be used to prepare any tax return, but in some areas doesn't provide as much hand-holding as the higher versions.
If you qualify AND if you wait until mid January THEN you can use one of the 10 IRS FREE FILE options to file a fed & state return for free ... but you must be patient. https://www.irs.gov/filing/free-file-do-your-federal-taxes-for-free
IRS Free File: Closed until January 2021
IRS Free File is closed for the 2020 tax season. Check back in January for Filing Season 2021 opening details.
For Filing Season 2021, you must make $72,000 or below to use one of the 10 IRS Free File partner offers.