I was arrested on a felony gta (because of a rental car and spent 3 days in jail. The felony was dropped to a misdemeanor and I was released on o.r. I went to court and was order to pay the Enterprise the rental fee and that was that. Will I be able to pass a department of justice background check? This was 2 years ago.

I will assume, that when you "paid" for the rental car, one of two things happened.
1. They dropped charges
2. you really plead guilty in a plea deal and paid for car. (you may not have understood the wording they used, for this.

So, for that, you need to clarify what happened, and perhaps should review those court records.

Also, how was the question for DOJ worded, when I did mine, it asked if I was ever arrested, not just convicted.

They will see the arrest, they will see the charges reduced and will see the final outcome.

As long as you told them about what happened and was honest, it should be fine, Most DOJ are rejected because people do not admit to what they did.

If it was dropped to a misdemeanor then you have a conviction for a misdemeanor. If that charge was dropped as well then you answer no about having any criminal record or ever been convicted of anything. If they ask about arrest then the answer is yes.