After you file

For the years you filed a Form 1040 when you should have filed Form 1040 NR, you need to file a Form 1040X amended return with a Form 1040-NR attached. 

First, you will need to prepare a Form 1040-NR tax return, which you cannot do in TurboTax.  SprintTax is a software that can prepare a Form 1040-NR.  Once you have prepared the Form 1040-NR, you can print and manually complete the Form 1040X at this link, using the instructions shown below (from Form 1040X at this link).

Resident and nonresident aliens.

Use Form 1040X to amend Form 1040NR or Form 1040NR-EZ. Also, use Form 1040X if you should have filed Form 1040 (or, for years before 2018, Form 1040, 1040A, or 1040EZ) instead of Form 1040NR or 1040NR-EZ, or vice versa.

To amend Form 1040NR or 1040NR-EZ, or to file the correct return, do the following:

• Enter your name, current address, and social security number (SSN) or individual taxpayer identification number (ITIN) on the front of Form 1040X.
• Don’t enter any other information on page 1. Also, don’t complete Parts I or II on page 2 of Form 1040X.
• Enter in Part III the reason why you are filing Form 1040X (e.g., filed Form 1040 instead of correct Form 1040NR).
• Complete a new or corrected return (Form 1040, Form 1040NR, etc.).
• Across the top of the new or corrected return, write "Amended."
• Attach the new or corrected return to the back of Form 1040X.

I haven't seen specific IRS guidance on your stimulus payment question, but probably not until you are classified as a U.S. resident alien and have a a social security number valid for employment.  Whether the "U.S. resident alien" tests in Publication 519 will be applied for stimulus payment has not been clarified.

You can start counting days of physical presence in 2020, and once you have been present 183 days you will meet the Substantial Presence Test to be a U.S. resident alien for tax purposes. Under that scenario, you will be a U.S. resident for tax purposes on the first day you were present in the U.S. during 2020.  

To be eligible for a stimulus payment, you must meet these eligibility requirements, according to the IRS Economic Impact Payment Information Center website at this link:

• Are a U.S. citizen or U.S. resident alien;
• Cannot be claimed as a dependent on someone else’s return;
• Have a Social Security number (SSN) that is valid for employment (valid SSN); and
  • Exception: If either spouse is a member of the U.S. Armed Forces at any time during the taxable year, then only one spouse needs to have a valid SSN
• Have adjusted gross income below an amount based on your filing status and the number of your qualifying children.