Are there any traffic infractions that would violate an ACD?

It depends on the specific conditions attached to your ACD but generally it would not.

Hello, my friend has to go back to court on thursday to pay a fine for a traffic violation and show that she completed the ddp

She probably has to appear before the judge again.

NY DMV keeps stating I have unpaid tix but the courts tell me I don't.

Go to enforcement division in DMV and demand ticket info.

What can I do to not get my license suspended or revoke

The only way is to avoid a conviction for speeding ticket. An attorney is the best way to do that.

I got a ticket for aggravated unlicensed operation. I did not know my liscence had been revoked. Can I argue the case at my h

you need to retain counsel and resolve the matter. I suggest a trip to DMV and speak to the the people in the enforcement division to see how to...

Unfortunately you need to get past the clerk. If they said need an attorney you may be stuck.

What to plead ?

Absolutely plead not guilty. You are lucky there exists the possibility of pleading it down.

Can a police officer selectively give out tickets when he pulls somebody over?

He gave the driver a break. That does not affect your father's guilt or innocence

Traffic court

I assume they charged you with permitting unlicensed operation of a motor vehicle. You likely can get the charge reduced.

Disobeyed traffic device should not count as a speeding violation. There must be more involved.