This paper studies the advanced methodologies of differential cryptanalysis with a particular emphasis on higher-order differentials and higher-order differential-linear cryptanalysis, along with their application to the ChaCha stream cipher. The study focuses on the impact of higher-order differential cryptanalysis on different rounds of the ChaCha stream cipher and analyzes how the cipher resists higher-order differential cryptanalysis. Additionally, we apply higher-order differential-linear cryptanalysis to target the reduced rounds of the ChaCha stream cipher, achieving reduced time complexity compared with existing studies. Furthermore, we introduce the first-ever higher-order differential-linear attack on ChaCha 6 and ChaCha 7 with 239.07 and 2135.07 time complexity, respectively. We substantially enhanced the attack complexity by a margin of 211.93 on ChaCha 6 and 231.82 on ChaCha 7. Moreover, for the first time, we report we report significantly larger higher-order differential biases of ChaCha, which were previously unknown for internal rounds beyond 3.5 rounds. Furthermore, this research reveals new linear approximations of certain bits from the 4th to the 6th and 7th rounds, thereby reducing the complexity of the distinguisher attack on the 5.5th, 6th, and 7th rounds of ChaCha.