I pray you are well
1) If a Muslim receives a fatwa with shariah ruling etc. And he thinks to himself that does he agree or disagree with the fatwa. Then thinks to himself that he agrees with it.
Does thinking in the first place, 'that does he agree or disagree with the fatwa' make him a kaafir?
The muslim has no intention of kufr and has no intention of disagreeing with the shariah law.
الجواب وبالله التوفيق
From the details mentioned in your question one does not become a kafir; however, you should perform repentance and astaghfar as due to such things there is fear of dying without eeman. Along with repentance and astaghfar, you should read the following dua:
(رضیت باللہ ربا و بالاسلام دیناً و بمحمد نبیاً (صلی اللہ علیہ وسلم
واللہ اعلم بالصواب