I need to know if "Dwesha" anger and fear are connected according to the Buddhist teachings? Also how to overcome fear or phobias with the practices of Buddhism?
Anger, Fear, Jealousy are all instances of the 2nd root of evil, 'Dosa', which translates to English as 'aversion'. They basically represent a disliking towards someone or something. Usually if it's someone more powerful than you, the disliking turns into fear. If not, it becomes anger.
Anger is mostly caused when you expect things to behave according to your liking. Fear is caused when you cling to things, taking them as I, me or mine. To overcome fear, you can recollect the virtues of the Triple gem and feel confident that you have taken refuge under them. But the permanent solution is to do Vipassana meditation and get rid of your clinging and the notion of self.
When one attains the state of Anagami, neither anger nor fear can ever enter one's mind again.
Here is what Buddhism says about how fear and anger are related. http://buddhism.about.com/od/basicbuddhistteachings/a/anger.htm
Buddhism teaches us that anger is created by mind. However, when you are dealing with your own anger, you should be more specific. Anger challenges us to look deeply into ourselves. Most of the time, anger is self-defensive. It arises from unresolved fears or when our ego-buttons are pushed.
As Buddhists we recognize that ego, fear and anger are insubstantial and ephemeral, not “real.” They’re ghosts, in a sense. Allowing anger to control our actions amounts to being bossed around by ghosts.
Anger Is Self-Indulgent
Anger is unpleasant but seductive. In this interview with Bill Moyer, Pema Chodron says that anger has a hook. “There's something delicious about finding fault with something,” she said. Especially when our egos are involved (which is nearly always the case), we may protect our anger. We justify it and even feed it.
Buddhism teaches that anger is never justified, however. Our practice is to cultivate metta, a loving kindness toward all beings that is free of selfish attachment. “All beings” includes the guy who just cut you off at the exit ramp, the co-worker who takes credit for your ideas, and even someone close and trusted who betrays you.
For this reason, when we become angry we must take great care not to act on our anger to hurt others. We must also take care not to hang on to our anger and give it a place to live and grow.
Fear can lead to anger and can also lead to lashing out at others in order to "protect" our self, as though it is vulnerable to another.
And here are some of the precepts to deal with and overcome anger http://buddhism.about.com/od/basicbuddhistteachings/a/anger.htm
How to Let It Go
You have acknowledged your anger, and you have examined yourself to understand what caused the anger to arise. Yet you are still angry. What’s next?
Pema Chodron counsels patience. Patience means waiting to act or speak until you can do so without causing harm. “Patience has a quality of enormous honesty in it,” she said. “It also has a quality of not escalating things, allowing a lot of space for the other person to speak, for the other person to express themselves, while you don’t react, even though inside you are reacting.”
If you have a meditation practice, this is the time to put it to work. Sit still with the heat and tension of anger. Quiet the internal chatter of other-blame and self-blame. Acknowledge the anger and enter into it entirely. Embrace your anger with patience and compassion for all beings, including yourself.
Don’t Feed Anger
It’s hard not to act, to remain still and silent while our emotions are screaming at us. Anger fills us with edgy energy and makes us want to do something. Pop psychology tells us to pound our fists into pillows or to scream at the walls to “work out” our anger. Thich Nhat Hanh disagrees.
“When you express your anger you think that you are getting anger out of your system, but that's not true,” he said. “When you express your anger, either verbally or with physical violence, you are feeding the seed of anger, and it becomes stronger in you.” Only understanding and compassion can neutralize anger.
Compassion Takes Courage
Sometimes we confuse aggression with strength and non-action with weakness. Buddhism teaches that just the opposite is true.
Giving in to the impulses of anger, allowing anger to hook us and jerk us around, is weakness. On the other hand, it takes strength to acknowledge the fear and selfishness in which our anger usually is rooted. It also takes discipline to meditate in the flames of anger.
The Buddha said, “Conquer anger by non-anger. Conquer evil by good. Conquer miserliness by liberality. Conquer a liar by truthfulness.” (Dhammapada, v. 233)