How do the Dwarf’s help?  What is their goal? 

They didn’t get away and preferred to stay and kill as many as of both they could. Their goal is to want Narnia for their own.

Where do Tirian and his group find a refreshing drink of water?  

They had found a trickle of water coming down the rock  

Once the Last Battle begins, what factor gives the enemy an overwhelming advantage?  

Spears. The Calormnes had spears that make all the difference.  With a long spear, you can kill a boar before you are in reach of his tusks and a unicorn before you are in reach of his horn

Once Tirian realizes this, how does he respond?  Does he give up?   What does he do with the Tarkaan?  

Even though this bad situation, he was still fighting for their lives.

No, he never gave up.  He only thought was to sell his life as dearly as he could to fight furiously to the enemies.

He was fighting the Tarkaan as hard as he could. And the next, he dropped his sword, darted forward and seized his enemy by the belt with both hands, and jumped back into the stable.