Basically, when my wife and I became married, we only a few days after found out we did the marriage ENTIRELY wrong. And in the time that we thought we were married, we did not have intercourse. But as soon as we found out we did it wrong the day after we repeated the nikah but correctly. My first question is, were we wrong to redo it so soon afterwards?
We both repented, but I'm scared I myself may not have been sincere because we redid it again so soon afterwards.

I couldn't remember saying "Bismillah" on our first nikah, but I couldn't see why NOT saying it. My wife said she remembered me saying a lot of stuff, and was certain I said it, though she couldn't remember it either. From my knowledge, just being confident you did something is enough. But what if we DIDN'T actually?

What about the mehr? I've been having waswas about that too.

I've been worried about whether or not we vocally mentioned the mehr just before or just after the nikah. We both already knew what the mehr was to be months before the nikah, but does it make a difference if we didn't mention it during the actual nikah?

1- By redoing it right away, you made the right decision. You discovered it wasn’t done correctly, then you did it correctly. There is absolutely nothing wrong with that.

2- Allah is very merciful. Don’t be terrified for something that isn’t sinful, and it was not deliberate to begin with.

3- The Imam will not perform any hudud on you. Rest assured. What you did does not warrant any hudud according to Allah’s law.

4- You don’t have to redo your nikkah. It’s perfectly valid since you have already performed it correctly. Don’t delay consummating the marriage. Enjoy the marital relationship together and start a new, positive chapter together with Allah’s blessings.

5- Bismillah is not mandatory to recite for Nikkah

6- As long as you agreed on a mahar, you’re good. You would have to give her that mahar. If she changes her mind, you are not obligated to give her another mahar. You can willingly if you want to.

7- You have to giver her the mahar whenever you are able to. As long as she’s no demanding it, you’re fine. Regardless the Nikkah is valid.