Is saying, "I will not deal with him neither in my heart nor by Islamic Sharia," considered an act of disbelief (kufr)? And is saying, "Even if you were to place your hand in the hand of Allah, I would not change my mind," considered an act that expels one from Islam? If so, what are the implications for the marriage contract? And is the intention sufficient to renew it?

The word you uttered is not disbelief (kufr); rather, it is reprehensible because it indicates a lack of adherence to Islamic law (Shari'ah). However, if it was merely a fleeting thought (a whisper), then it is forgiven, and you should not dwell on such intrusive thoughts.

As for your brother's word, it is undoubtedly disbelief, as it attributes incapability to Allah the Almighty. You must advise him to repent from it. Regarding his marriage, he may follow the opinion of those who do not deem its renewal necessary. If he wishes to renew it, the matter is simple: the guardian can remarry him in the presence of two witnesses.