The first part of the question is basically, would the Opium Wars or Chinese history in general be any different if the rebellion didn't happen?

The First Opium War happened before the Taiping Rebellion. The resulting Western influence in China and the outflow of silver from China is one of the major reasons why the Taiping Rebellion broke out. As for the Second Opium War, it's kind of hard to say. The rebellion did prevent Qing officials from successfully defending Guangzhou from the Anglo-French forces, but given the gap in military technology between China and the Europeans, I think it wouldn't have made a difference. As for whether or not Chinese history would be different, well of course it would be different. Millions of people wouldn't have been killed or displaced. The rise of powerful Han officials probably wouldn't have happened as fast. But this really goes into speculative history, which is not allowed in this sub.

The second part would be, is it perceived as a part of the general foreign Western incursion into 19. century China or a separated event?

The Taiping were psuedo-Christians. They were heavily influenced by Christianity, which came to China as a result of Western incursions in the 19th century.

Also because the wikipedia article mentions a nationalistic anti-Manchu/anti-Qing element as being one of the driving forces of the rebellion, is there any sort of positive interpretation of this rebellion in modern China despite it being Christian, considering how negatively the Qing dynasty is viewed?

Yes. Sun Yat-sen had mixed views about the Taiping. He praised them as early pioneers in the people's revolution, especially for their opposition towards the Manchus (anti-Manchu propaganda and Han nationalism was heavily used by the revolutionaries themselves). He compared their leader Hong Xiuquan to Zhu Yuanzhang, the founder of the Ming, who was also fighting to overthrow an alien regime (the Mongols). He did, however, criticize them for their autocratic form of government. Chiang Kai-shek also wrote that the "history of the Taiping Heavenly Kingdom is a glorious period in the history of China during the 19th century."

Within Mainland China, views of the Taiping are generally favorable. This is in large part due to several Taiping policies being extremely similar to CCP policies. Luo Ergang's History of the Taiping Heavenly Kingdom summarizes these key points:

• The Taiping were generally considered to be proto-revolutionaries who fought against Western imperialism and feudalism, destroying the idol of feudalism - Confucius.
• The Taiping laid the groundwork for the Xinhai Revolution. The rebellion completely destroyed the Eight Banner system and the Green Standard Army, leading to the rise of powerful Han officials such as Zeng Guofan, Li Hongzhang, Zhang Zhidong, and Zuo Zongtang. Li Hongzhang himself was instrumental in the rise of Yuan Shikai, who ultimately ended the Qing Dynasty.
• The Taiping pushed for the development of a productive society by abolishing private ownership of land and redistributing it, not dissimilar to the CCP's "land to the tiller" land reform movement of 1953. The Taiping also abolished social classes, promoted gender equality, allowed women to be educated, and outlawed polygamy, prostitution, and footbinding, which were all policies of the CCP as well.

Of course, this is not the orthodox view of the Taiping in Mainland China, and there continues to be debates about it.