Your employer's attorney will know what boxes to check on the petition.
Yes, you have to request a change of status.
You are in a situation called "bridging"
Lawyers are familiar with how to handle these situations so you don't need to worry about it.
Does this means I will have two change of status petition with USCIS. One which I already submitted F1-F2 and other which will be my H1B petition? or my new H1B petition override my old F1-F2 COS petition?
If this does not override old F1-F2 VOS petition, that means I need to wait 5 months for F1 to F2 petition and then 5 more months for H1B?
No the new H1B does not over-ride the pending COS request.
Yes, your COS request takes approx 5 months which will come up while the H1B is filed and pending on April 1st. Regular processing can take as I said "UP TO 5 MONTHS". If it is a clear case of direct employment it can be approved sooner because there wouldn't be an RFE sent out.
You seem to be stressing unnecessarily so far in advance. You don't even know if your H1B petition will be selected in the lottery. You need to take things one step at a time and not be in a panic before hand.
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In the future, you may begin your questions with “FOR JUDITH” and I will be your personal immigration expert.