Can alcohol use at a young age damage your brain more than as an adult?

Yes. The developing brain is more sensitive to the effects of any drug which can damage the brain, including alcohol, cocaine, amphetamines, as well as marijuana. In addition, the earlier one drinks, the more likely that person is to develop more serious problems with that drug and others as they get older. Those who start alcohol before age 13 are many times more likely to have problems than after 17.
Yes. The effects of alcohol, like most drugs, are dose dependent. A sip of wine is unlikely to hurt anyone, but getting rip-roaring drunk can cause damage. That said, when a person is younger their brain is still developing, sometimes into their twenties. It stands to reason that a brain that is still developing will be more affected than an adult brain. All the more reason for kids to avoid alcohol.