How can I continue to live , work and pay taxes in the USA (NY)? Do I sponsor myself?

Your business may be able to sponsor you. You need to schedule a consultation with an experienced immigration attorney.

Which PDF editor lawyers use and can I write remaining character by hand that won't fit on computer?

different fonts even partially hand-written entries are fine.

Which I -94 number is correct the one that shows online or from H-1B approval notice?

Use the I-94 you retrieve from the CBP.gov website.

How long does the process take? Can I travel to the US on a tourist visa while my application is being processed?

You can but I would advise against it if you have an H-1B petition pending as it may cause issues when you return tot he USA as to our intent.

Is my new lawyer recommending the right course of action or can we file new petition without problem?

If employers change then a new H-4 should be submitted especially if your period of H-1 authorized stay will be changed.

Sponsoring after marriage

For sure your spouse and then a joint sponsor if necessary.

How much longer should I wait?

Sometimes in cases like this it is much easier to just refile the I-130 petition.

Can I get an extension on I 751 marriage based conditional green card when I have already got one year extension previously?

Infopass will not help you. You need to speak to an attorney to advise you properly.

What should I do?

One option which I have successfully used on behalf of my clients is getting a local congress person or Senator involved.

It could be anything - maybe some docs were missing regarding the affidavit of support. You need to wait and see what they are asking for.