So you had several questions, see answers below:

How can an illegal adult, brought to US as a child of 6, obtain legal status in US?

It would depend on if they qualify for 245i. Would need more info.

What are legal fees for immigration help?

It depends on what they would qualify for. Try for a legal consultation first to see what they are eligible for.

Can the Dream Act pass?

It is possible.

Additional Details:
Would this adult be protected against being deported during the process of finding a legal status?

No guarantee. Need more facts to see what they are eligible for.

Would attorney/client privilege protect the adult?

It protects communications not a person from getting deported.

How likely is the Dream Act to be approved?

It has been introduced for 10 years in a row, and has failed to pass as of yet. Will have to wait and see.

Would a ten-year-old sister, born in the US qualify as a family member with US citizenship who could sponsor the adult or does the US citizen have to be an adult?

The sister can file for the brother when she is 21 years old or older. However, 245i again is going to be the issue of whether the beneficiary is eligible for adjustment.