Answer to Question 1
Generally speaking, fear is the emotion we feel when there is concrete danger, such as the feeling of fright you have when suddenly encountering a growling large muscular dog in your flower bed. There is a very real possibility that you could receive some unwanted tooth marks on your leg as that scenario unfolds. So your fear is well founded.
On the other hand, anxiety involves more complex and diffuse feelings of uneasiness related to possible impending threats. Anxiety is very future oriented and can capture more abstract threats than fear (e.g., the anxiety of losing face in front of an audience). We often use words like nervous, apprehensive, and uneasy to capture the anxiety emotions. Worry involves mentally recycling concernsit is the process of repeating our thoughts associated with anxiety.
Answer to Question 2
There is considerable evidence that engaging in aerobic exercise will boost the feel good chemicals in your brain and also reduce anxiety that often accompanies depressed moods. Being on a regular exercise routine can also be used as a preventative strategy for reducing the likelihood or frequency of future depressed moods. In fact, depressed moods can be motivators to strengthen your desire to also implement other healthy lifestyle strategies such as healthy eating and using stress management.