Let's say you have a job as a waiter, and stash away some of the cash
you make in a separate bank account. The tax folks audit you -

1) Can they do a search on your name to see how many total bank
accounts in your name exist in the US?

2) If yes, what type of an information system/database do they use to
find all the bank accounts in your name?

3) Is there any way to have a separate bank account that can be setup
keeping it private from the tax folks? The common glue is your ssn, I
assume.

You should try to avoid illegal activity.  That's how people end up in jail.

1.  If the IRS audits you, the IRS will pull all financial records for
the current year from all financial institutions.  They will check
cash in flow compared to earnings your reported on your 1040.  If they
have even the slightest evidence from this top level overview that you
might be underreporting income they will conduct an in depth analysis
of your actual earnings to reported earnings.

2.  Every financial transaction a consumer makes is stored into a
database at the financial institutions involved.  The IRS, being a
government entity, has access rights to all of these in an
investigation.

3.  Depositing cash into different State based accounts, or even
wiring cash outside the country is easily tracked by the IRS. 
Citizens leave a paper trail everytime a financial
transaction/transfer is made that the IRS can gain access to.

All earned income should be reported to the IRS.  If you are caught
trying to hide income you will be assessed penalties and interest on
your tax liability from previous years.  As a citizen of the United
States that enjoys the many liberties and services provided by the US
government you should pay taxes for the benefits received.