In a five sector model, that includes the household sector, business sector, financial sector, government sector and foreign sector. What is the correct economic term for the model/graph?

The correct economic term for this model/graph is a circular flow of income model.

The flow from the financial sector to the government sector is called what? And is it a leakage, injection or neither of them?

The flow from the financial sector to the government sector is often referred to as government borrowing or taxation. This flow represents a leakage from the circular flow of income, as it redirects money away from the flow of income between households and businesses. So, in this context, it would be considered a leakage.

From the government sector to the financial sector?

The flow from the government sector to the financial sector would typically be associated with government spending or investments, which inject money back into the economy. Therefore, in this context, the flow from the government sector to the financial sector would be considered an injection into the circular flow of income.