Do people who have had a brain tumor and brain surgery to remove part of the tumor removed qualify for benefits?

It's very possible.  You should consult with an attorney who specializes in Social Security Disability. 

Eligibility for benefits turns on inability to perform any job, not just your previous job, which is expected to last for at least 12 months or result in death.  Education and age are taken into account.  You can apply and, if necessary, apply for reconsideration and redetermination at www.ssa.gov.  If you must appeal to an administrative law judge, you can be represented.  You can find an attorney who specializes in this area on the website of the National Organization of Social Security Claimants Representatives.