Can alcohol alter your brain chemistry?

Yes. With acute intoxication the brain chemistry is altered, alcohol withdrawal, brain chemistry is altered and if dependence to alcohol develops, brain chemistry is altered. Any drug including alcohol has a direct effect on the brain, its neurotransmitters, it may cause some neurotrasmitter levels to go up and some to go down. The brain "tries" to adapt to what you do to it, but their are consequences.
Yes. That's actually what it does and that's what being drunk or intoxicated is - an alteration of our brain chemistry. It acts on receptors that inhibit nerve transmission; the earliest inhibition is in the very front of the brain where our inhibitions and judgements are stored, so we may get silly and more social. The higher the dose, the more sedation, and in very high doses sleep, coma and death.