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.
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 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.