Yes, for US tax purposes, you should file Married Filing Separately because neither of you is living in the United States. You won't be able to file Head of Household because your children aren't residents of the US. Don't report your children on your tax return. If it asks if you have dependents, say none.
Leave the SSN field blank or write "NRA" (Non-Resident Alien) in the space provided. This tells the IRS that your spouse is a nonresident and not eligible for a number, per the IRS in this link.
To claim your retirement contribution, you generally don't need to take action on your part. This is shown in Box 12 of your W-2, with code D and the amount of the contribution. As a result, the amount of the contribution is reflected in Box 1 of your W2. You may verify this by comparing Box 1 with Box 3 of your W2. If Box 3 has a higher amount listed, the difference is the amount of your 401K contribution.
You may receive your refund either in a paper check or a direct deposit. You will have that option to choose after you prepare your return and you are ready to file.
TurboTax software doesn't file non-resident 1040 NR tax returns. Our affiliate at Sprint Tax does. Please contact them for further help here.
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