About a month ago I purchased a New 22A. Yesterday I was shooting and then all of the sudden it had a failure to feed issue on every bullet. After inspection we found that the firing pin broke in half! Is this a common problem with the 22a?

That sounds weird for it to break with that few of rounds. They will fix it of course but need to find out why it broke. It is a easy fix and they may just send you a new firing pin or have you take it to a repair center so they can see why it failed.

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I don't own your pistol, but I have read other posts that have stated that dry firing is not good for rimfires. You did not say how many rounds you fired, but that's not important at this time. If it's a broken pin, it's a broken pin.
What is puzzling to me is that you said it failed to feed. I take it that it fired and didn't feed after you fired it. Is that right? That's a strange situation with a broken firing pin.
In any event I would send it back to S&W for evaluation. Could be that something else could be amiss with your pistol that could have caused the pin to break in the first place.
Good luck.

It has about 600-700 rounds through it if not more. It would fire, but it would not feed the next round as the firing pin was getting hung up on the round as it wasn’t moving properly.

I only discovered today that you should dry fire this gun. I did dry fire it many times. I am guessing that is the cause.

Yes you shouldn't dry fire a rimfire gun. You should also check the edge of the chamber where the firing pin hits, sometimes you can raise a dimple that will cause the gun to slam fire as it chambers a round.