I will address your initial question with some ideological context. I will also address your second question. I hope someone else can help with the other two questions you've posed! Also, I'm sorry this is a giant wall of text! Brevity is something I struggle with.

In R. Keith Schoppa's book Revolution and It's Past: Identities and Change in Modern Chinese History, Schoppa dedicates most of a chapter to this question. Schoppa begins with the following:

Chinese culture had always focused on the past. Even for Confucious the golden age had been in that past, a time when society was harmonious and the country was peaceful. The goal of statesmen throughout the centuries was to restore something of that splendid past, even though no one thought that it could ever really be done. The past framed the present, so any change in state and society had to be rationalized in terms of that past, whether the particularly relevant past was the policies of a recent emperor or one's family traditions.

I think that this is one of the obstacles that the Qing encountered in regard to westernization. It is also worth noting that people who were part of the 'self-strengthening' movement subscribed to the idea that they could convince conservatives that Western weapons were only inanimate machines. They were able to rationalize that the weapons were culture neutral. They were the means by which China could protect their culture. Schoppa argues that this logic contains a glaring fallacy:

Foreign machines might look culture neutral (i.e., anyone can turn a switch, pull a trigger, or pilot a ship), but they came with a host of culture-specific scientific views and worldviews.

Essentially, if a young man were to begin the study of engineering and technology, that student would return to Chinese culture with a new set of worldviews. When applied to the Chinese classics, these worldviews would provide a broader context for the content and more questions would arise. This was a threat to the revered classics and basis for Chinese society.

Another problem encountered was the problem of the civil service exam. Until this time, success was measured by the civil service exam. Officials were concerned that they would not be able to attract students to the shipyard schools or arsenals because the best students trained for the civil service exam. How would the government be able to persuade good students to apply to schools which taught concepts that were not tested on the exam. Schoppa cites Li Hongzhang:

One of the measures we can take is to introduce a new category in the civil service examination, namely the category of technology.

Additionally, I have notes from a course I took on Modern China. The professor advised that China did not have the infrastructure to maintain modernization. I don't have more information to support this assertion unfortunately.

Most of the following is sourced from Schoppa's book and that lecture I mentioned above. This is a basic chronology of the indemnities paid by the Qing and little bit about taxes.

I think that to fully understand the economic problems of the late Qing, we must start with the reign of Qianlong. The Qing essentially took over the Ming tax system and did not reform it or reassess taxes. One might imagine that this was a mistake. Taxes were paid in silver taels. Farmers would trade their crops for copper and, in turn, trade those for silver taels. Here are some statistics regarding taxes that I find startling.

During the reign of emperor Jianqing (1769-1821) 1 tael equated to 1500 copper During the reign of emperor Daoguong (1821-1850) 1 tael equated to 2700 copper

In 1834 the British East India Company went bankrupt. China traded heavily with the company. The Opium War ensued. It lasted from 1839-1842. The Treaty of Nanjing signed by Great Britain and the Qing opened the ports of Canton, Ningbo, Shanghai, Xiamen, and Xenjiang. It also relinquished Hong Kong to the British. A total indemnity of 21 million pounds was to be paid by the Qing before 1941 in installments. The British charged 5% interest on late payments.

At this point, the general consensus of the public regarding taxes was "the government doesn't help me, so I won't pay my taxes!" By 1864, the treasury is bankrupt. The Tianjin massacre of 1870 ended in an indemnity to the French for 20 million taels. The First Sino-Japanese War ended in 1895. The Treaty of Shimonoseki established an indemnity to Japan for 200 million taels and the Qing gave up several key pieces of territory.

The Boxer Rebellion resulted in another indemnity of 450 million taels ($333 million in 1901). Schoppa notes that the average yearly income for the Qing at this time is only 88.2 million taels in 1901.

Eventually, the Qing dissolved the ineffective Bannerman army. Once violence erupted, they asked wealthy citizens to raise money and troops to protect the royal family. The final straw in my opinion were the train lines. in 1869, China had approximately 370 miles of rail lines. The Qing needed investors for the rail lines. Many foreign companies invested. Specifically, Germans created shell companies to invest in the rail lines. The fatal blow came in 1910. The Qing decided to nationalize all of the rail in the country. Schoppa notes that this is a last ditch effort to save themselves.

The Qing government was not in a good economic situation near the end of the dynasty. You can reason that individual Qing officials had wealth, but the government in general was in a very bad place economically. I hope this answers your question! If you have further questions, I will try my best to answer them!