I have a US checking account only (no saving account) and I have no interests on the money in this account. I have left US on 12/01 and my job in US ended on 11/30. By keeping this US account open, would I need to file a tax return also in 2019?

No, you would not need to file a nonresident return in 2019 even if you had bank interest from a US bank, unless the interest is connected to your conduct of a US trade or business.

https://www.irs.gov/individuals/international-taxpayers/nonresident-aliens-exclusions-from-income

Please Note:  If you are filing a return in TurboTax, you are filing a full year resident return.  As such, you must include your worldwide income from January 1 to December 31, 2018.  If you earned income in December after leaving the US, you need to report that income on your US tax return.  You can use foreign tax credit to offset any double taxation.

Let me know if you have any questions.

I had a salary paid in December from a foreign employer.  Should I have to report it in the tax return and where? What should I do to offset any double taxation?