My mom is always angry. Does this mean that something is wrong with her mentally?

Not sure. Not necessarily, but possibly. Some people with depression, bipolar disorder, and some personality disorders are very irritable and get angry easily. Sometimes people with chronic pain are that way too. If you're noticing a change in your mother, encourage her to see her physician and figure out what's going on. Chances are she's not happy either, and might like the chance to feel better.
Not necessarily. It sounds like you are worried about your mother. Do you get along well enough to risk asking her why she seems so angry all the time? Do you feel you are the cause of her anger? Anger is usually a sign of great stress. What kind of stress is she under - financial, family problems, depression? Do what you can to help and encourage her. Let her know you care. Have you suggested counseling? Do!