would this cause any issues filing for a green card through spouse after marriage? would the overstay cause any issues?

If you marry her, your overstay does not matter and you can successfully adjust your status.

Processing time for Green Card/EAD for someone in F1 OPT status married to US citizen??

EAD generally takes up to 90 days. I also agree with my colleagues that you need to talk to an immigration attorney.

Can employer legally pay the filing fees for I-485 and Premium Processing Service?

They can pay the fees if they want too. If they are small company most likely they will not.

I 140 - H1 extensions - Multiple employers

Yes. As long as the I-140 is valid. Good luck.

Can i do Invitation of letter to attend religious rites for my wife and kids?

I agree with my colleagues. It might be too late for now.

I agree with my colleagues here. The visa that you hold is employer specific.

Unfortunately not. I-140 petition works with the future employer. You cannot adjust your status based on an employer who does not exist.

You cannot go out of status if you want to adjust your status.

Will I be out of status?

While on Grace Period, you will not go out of status. You can apply for OPT. Work closely with your DSO.

My query is that can I travel outside US in july and come back in august,while my extension is in application process. Thanks.

Contact the attorney of the record.