What should i opt for? Will my F-2 visa be cancelled if F-1 visa is denied in my home country?

Talk to your DSO. They should be able to help you free of charge.

Travel outside USA on H1B within 6 months of visa expiration

Refer your concerns to the counsel of record.

Just be patient. It means that your case has been approved.

How long will it take for Green Card process - Family Fourth Preference for me , being from country Nepal?

Around 12-13 years. Check the visa bulletin.

Entering USA with H4, after H1B picked in lottery

Talk to the attorney who filed your H4/H1B.

Is my attorney prohibited from calling USCIS for 30 days since I called them?

I agree with my colleagues. Good luck.

Could you please tell me if I have any chances to apply for Green Card for NIW process?

It is highly recommended that you speak with an immigration attorney in private. You may have a good chance for NIW. Good luck.

I agree with my distinguished colleagues.

As an H4 visa holder , can I start a meetup group and charge a fee ?

You need a valid EAD. Otherwise no.

Can I travel to the US with the amendment receipt notice before the amendment is approved?

If you have valid visa, then the answer is yes.