Q:

Questions about multiple particles 「が」 in a sentence

Here is the sentence said by a boy who had punched a pig in a pen and then being struck by it.
だめだっ...なぐろうがけとばそうがびくともしやせん
1) Does the first 「が」 work the same function as the second one?
2) Can I replace the first 「が」with 「と」 or 「や」 to list multiple actions: 「なぐろう」 and 「けとばそう」?
3) Based on the understanding the multiple particles in the sentence, I translated like this: 'Even I intend to hit and kick the pig but it's not  afraid of me at all', am I correct?

A:

What he is saying in this sentence is,

「だめだっ...なぐろうがけとばそうがびくともしやせん」
Its no good, its doesn't matter if punch
  or kick him/it nothing affects him/it. 

Yes, 「が」is working the same function in this case.
And to answer the second question, you can't replace the first「が」with 「と」or 「や」.
This another way to re-phrase this.

だめだっ...殴{なぐ}っても蹴{け}っ飛{と}ばしてもびくともしやせん」

This basically has the same meaning, but the way I wrote it does not convey the emotion that the first sentence (your example) does.
The format is Verb「も」verb「も」, Basically, I did this as well as this.
EDIT. The comment from Chocolate, spurred me to elaborate a little more.
「びくともしやせん」does not carry the meaning of being scared, I am gathering that you were referring to 「びっくり」. In this case the meaning is that what ever you did to it (pig), nothing affected it. Or you could say it would not budge, flinch or move. Hope that helps.
Edit: Request for further explanation.
「殴{なぐ}ろう」 is the volitional verb form of 「殴{なぐ}る」

ビリーくんがチャーリくんを殴{なぐ}ろうとしたが、友達{ともだち}に止{と}められた 
Billy tried to punch
  Charlie, but [Billy's] friends stopped him.

「蹴{け}っ飛{と}ばそう」or 「蹴{け}飛{と}ばそう」 (both same meaning) is the volitional verb form of「蹴{け}っ飛{と}ばす」
and is a conjugated verb of 「蹴{け}る」and「飛{と}ばす」.「 蹴{け}っ飛{と}ばす」and 「蹴{け}る」both mean kick in this context of the sentence, but「蹴{け}っ飛{と}ばす」has the image of being more forceful and more powerful. In most case a verb that is conjugated with 「飛{と}ばす」, you are trying to emphasize the effect of the original verb.

ビリーくんがボールを蹴{け}っ飛{と}ばそうとしたが、足{あし}が滑{すべ}ってこける。
Billy tried to
  boot the ball, but he slipped and fell.

Here I am using "boot" as a more powerful word to "kick".
In these cases it is interpreted as try to do something. 
Another example.

ビリーくんが山を登{のぼ}ろうとしたが、足{あし}が滑{すべ}って落{お}ちた。
Billy tried to climb the mountain, but slipped and fell.

By its self you can do this.

ビリーくんが「あの山を登{のぼ}ろう」、とみんなに言{い}った。
Billy said, lets climb that mountain.

In this case it means lets do something.
「びくとも・しない」、with out getting too deep, it basically means to not budge, unyielding. 
It will always be「びくともしない」, you can't say this 「びくともする」.
I hope that helps.

