Everybody worries sometimes. Is it anxiety disorder?

No. Gad is an anxiety disorder that is characterized by excessive, uncontrollable and often irrational worry about every thing that is disproportionate to the actual source of worry. In this case the symptoms must last for 6 months and interfere with daily functioning.
Depends. As you said, worry is normal. Anxiety maybe excessive worry or worry for no reason. Anxiety may aslo be worry that is not consistent with the circumstances, and may interfere with your normal, daily, functions. To adequately answer your question, more information is needed.