I think "stubborn" work much better in both cases. 1. - My stubborn brain has been repeatedly making the same mistakes. 2. - The left side of my brain seems very stubborn, as it's making the same mistakes repeatedly. Stubborn and adamant are not interchangeable. Stubborn is a character trait. However, people are only adamant about a single subject (so he has a strong belief about something). For example, you could say "he was adamant not to lose" but you wouldn't say "he was an adamant person" (although you can say "he was a stubborn person").

Chinese does this too. Puts whole clauses before the noun. Thankfully Thai and Indonesian put them after so I can kind of "think in English" when practicing those two languages. Hehehe :)

Japanese really is different from English in this case, because all "true" adjectives like 可愛い come before the noun and all phrases that we would call "relative clauses" in English come before the noun too, huh? This probably gives some native Japanese speakers a hard time translating something like 私がEbayで買った本 because "that I bought on Ebay" has to be placed after the noun in English instead. Of course, sometimes I have to really think about how to move stuff before a noun in Japanese because of this. Hehehehehe.

Some more examples of adamant: 1. He was adamant that we should learn Japanese before learning Spanish. 2. He was adamant that the company would be closing in the fall. 3. I can't stand his friend who is adamant that we will never learn Japanese if we continue to use the same methods of learning. -- More examples of stubborn: 1. I wanted to go to the park but Josh was being stubborn and just wanted to lie around the house all day. 2. He was too stubborn to admit that he had yelled at the girl for no reason at all. 3. My horse Prince was sooooooooo stubborn when we tried to load him onto the trailer the last time. In fact, it took us well over 2 hours to actually get him on the trailer. -- Nick is right here about how you can say a "stubborn person" but you don't really say an "adamant person". If you want to use "adamant" as an "adjective", then it needs to modify the noun in a relative clause instead with the thing that the person is adamant about being listed as well. For instance, "people who are adamant about learning Spanish before tackling French". See how it comes after the noun in a relative clause and also lists what they are adamant about? That is, they are adamant about "learning Spanish before tackling French." :) Hope this helps. I agree with both of Nick's corrections to your sentences so I won't repeat them here. :)