Can I file2016 taxes?

To complete and file a 2016 tax return using TurboTax you will need to purchase and download one of the 2016 desktop editions from this website - https://turbotax.intuit.com/personal-taxes/past-years-products/

A 2016 tax return can only be printed and mailed, it cannot be e-filed.

If I already purchased the 2018 tax product to begin filing but didn't finish it, do I have to purchase it again to be able to download the software?

@Slrminav   Did you pay for the Online version?  You can ask Customer Service for the download program to finish.

Contact Customer Service
5am-5pm Pacific Time Monday -Friday
https://support.turbotax.intuit.com/contact/

How to finish a return you started online

https://ttlc.intuit.com/community/prior-year-return/help/how-do-i-finish-a-prior-year-return-that-i-started-in-turbotax-online/01/26322

Yes, I paid for the online version. Customer service isn't open, so I was hoping there was a way to download the software without their assistance without paying for the same product again.