Is the EB-3 visa bulletin for nationals born in Pakistan current? The visa bulletin seems to indicates so.

You appear to be correct in reading the chart. Talk to the company's lawyer and not some legal assistant.

I agree that affidavits will help ... so will a DNA test.

I have an O Visa sponsored by one company and want to move to a different company.

Yes, this can be done. Of course, it would be wise to have an attorney file the papers.

No, they are not cap-exempt per se. Unless, as my colleague pointed out, it is a state university.

Can we transfer H1 from one employer to the other without having the Stamping done?

You will need a visa stamp to travel to the US. But, the stamp can be for the 2nd employer.

What is the procedure to move to industry jobs for me?

Yes, you appear to qualify for an 'industry' cap exempt position.

H4 to f1 conversion?

I read your post ... but don't see a question. Please explain.

There is no specific number. But, 200 transactions in a year is nearly 1 a day ... slow down & you should be OK.

How to I apply for a work visa/permit?

You need to be more specific. Does your father have an E-1?

Ask your joint sponsor to do a new I-864.