"In this hadith is Muhammad al-Bukhari writing that Umar bin Khattab (RA) is saying that he (himself) heard these things? "

Yes my friend he is saying that.

And about :
"I think about when someone do something and it doesn't turn out quite like they wanted it to and someone says, "but his intentions were good." Is it speaking of the weighing of your deeds in the hereafter?"

you must take the right bath when you have good intention
You can not use any mean necessary even bad one's and say i had good Intentions.
This is the islamic interpretation.

And thank you indeed for taking interest in studying islamic religion.
If you want any help i am here for you. upvoted and resteemed