"Nagashi can be used to destroy low rank earthen and wooden structures and even negate chakra on the ground to stop high ranked earth and wood techniques."
-From the jutsu description
As the description says, Nagashi cannot destroy something as powerful as the Golem's arm, only negate the chakra in the arm to cause it to fall to the ground as a pile of rocks.
Keep that in mind for future use, and definitely re-read the jutsu's you use as most have been re-written.
Fire Release: Great Dragon Fire Technique was not the best choice to defend against Wind Pressure Damage, due to the scaling of the jutsu. A large, powerful wind front vs five (albeit large) balls of fire that through rank will work, really won't if you thought about it. Though it still is fine for the purposes of negating the jutsu, maybe a large fire stream would have worked better or a rock wall even?
Quarter dome? It works but... too risky for a someone to use really...
and the second attempt at you using that lightning jutsu, there are many more to choose from, try diversifying your arsenal.
"But while the ground was crumbling and spiralling inwards, Hashi jumped into the air and shot three giant bullets of fire"
- Quote from your move Khallil
As soon as you even attempt to move onto another jutsu, especially so soon after activating the earth jutsu, the ground would stop turning in and most likely result in a failed attempt at the jutsu. Leave time for your jutsu to activate before rushing off to your next jutsu.
You won't be able to create that many pillars so quickly as to generate lift and launch you in the air, you are wearing a heavy suit or rock so you where best off staying put.
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Overall, the counters where a bit Robotic, having to counter with the correct element at the correct time, you both should start thinking of how to counter using the other elements.
Also:
Jiraiya:
D
C 2
B 4
A 2
S 2
Khallil:
D
C 1
B 8
A 7
S 4
Just a tally for the hell of it ;P
Anyway, you both did well in terms of throwing mid-ranged jutsu at each other, but I am disappointed that neither of you engaged in any closer range fighting. I realise this was to show skill in the Basic five, but nothing was stopping you intertwining that with freeform at close range. Try to spread both your skills out, stop relying on high ranked jutsu and think outside the normal "Fire beats wind" etc counters.
As for who I think showed better skill, Jiraiya for his use of the water element in the latter half of the battle.