[Q1. Military Success]

Saul was afraid of David because he was I believe entertaining darkness of his own. Maybe he thought that if he could David killed he would return to some sort of former glory.

David's wise behavior was key to Saul's fear of him. Saul could see David's wisdom and success and that the "Lord was with him" 
Saul knew the wisdom David was exhibiting was from the same source that had removed him as king. 

[Q3. The Battle Is the Lord's]

I truly wrestle with this one.  At times I feel that I am listening to the spirit and engaging in Gods plan and not my own. At other times I feel I am just the arm of flesh going though the motions. I know the key here is to recognize when I am in fellowship and when I'm not. Thank God I have His word which cuts though my thoughts and helps me to hear His voice.
All my heart, soul , mind and strength....Love breeding confidence breeding faith. No carnal mind can hold a match to it.

[Q1. Goliath's Taunt]

David could not stomach Goliath's taunt because of a few reasons:

1. David knew that Jehovah was the one true God
2. David knew that his election and calling were anointed by Samuel himself.
3. Spiritually David was feeling righteous indignation at the spewing of one so diametrically opposed to God almighty.

Eliab had some issues of his own. First of all he was looked over by Samuel and was genuinely jealous and afraid of David.  
He knew his brothers boldness would "show him up" . Eliab was faithless and not "king material" evidently.

[Q2. Experience and Faith]

wow what a question!

To begin with David truly thinks of himself as a part of the "armies of the  living God". That confidence right there is shown in his boldness of speech.

Davis is fearless and in that stance he becomes formidable as the agent of Yaweh.  I believe that the courage of David's conviction is contagious and inspires Saul to allow him to fight. If Saul has any faith now it is in the ferociousness of David.

[Q3. Anointing and Spirit]

Wow what a question. Samuel's obedience to anoint David with oil is so significant. David is now clothed with "dunamis" and can execute God's will with the eyes, ears, mouth and hands of God almighty. 

[Q2. Listening to the Spirit]

What to do?

Decisions, etc. Sometimes I am asked to pray for healing or asked what to do in a difficult situation. Making sure you are in fellowship with the Father and then believing that He will respond is key. Jesus kneeling down and writing in the sand was waiting for the Father to give the best answer possible. We have the mind of Christ.

[Q1. Rebellion]

Rebellion is actually the attempt to sit the seat of self alone and telling God that "you" are in charge. It is fueled by selfishness and executed with knowledge and aforethought.
To me that is like diametric opposition to obedience. Like witchcraft.

Arrogance is the switch that turns bad thinking into bad action.

I catch myself so often thinking that my flesh alone can solve a problem. "for the thing which I would not do, that I do..becomes my dilemma and I realize I am in that rebellious space. 

I have gone to God many times to tell Him my shame and ask for wisdom and humility.