Past F1 overstay, readmitted, eligible for AOS through marriage?

Yes you may be eligible for AOS through good faith marriage but for case specific inquiries, it is best to consult with an attorney in private.

This is not advisable particularly when one residence in outside of the US. You may not meet the eligibility requirements for citizenship so it is...

Sponsor documents required during AOS interview?

If you included yours as well, bring W2 and employment docs for both of you as well as jointly filed tax returns.

Filed n-400 on July 30th, and today is 8/25 and haven't gotten the receipt notice?

Yes some receipts, particularly when you submitted a fee waiver can take over a month.

Can I get a green card by marrying a Green Cardholder?

Yes it is possible but a review of your case must be done prior to an analysis.

Is it legal for a US Citizen through Naturalization to renew his/her birth country passport ?

It depends on whether that country allows for dual citizenship. Consult with an attorney for guidance.

It appeared I applied N400 online one day early. Withdraw my application?

You should wait and rely on the submitted case for adjudication.

Should I write my name in Russian or in Hebrew, when applying for US tourist visa (name in the native alphabet)

What is your native alphabet? If Russian, indicate accordingly.

Adjustment of status

Yes that should help with good faith marriage analysis and question of your intent. Consider consult with an attorney for guidance.

What kind of occupation I can choose?

You should be able to input your occupation/job in the appropriate section of the form.