Tax obligations for Canadian citizen doing business in USA, Delaware
Allow me to answer your questions one by one:
1. I presume your question related to whether you need to register your corporation in Canada as well. This question really depends on where your corporation is doing business. If it does business in the US you might not need to register it in Canada. If you plan to have physical presence in Canada you should research the question of registering it in Canada as well.
2. As far as taxation goes, for professional advice I would recommend you to seek an accountant specializing in international taxation of corporations. In general, US corporations are taxed at the corporate tax rate on income produced in the US, and in addition Delaware corporations are taxed on income produced in Delaware. If the corporation produces income in other countries it should be registered and taxed according to the laws of that country
Being a shareholder of a US corporation you would receive dividend and would be required to pay an appropriate tax on dividends in your country (Canada).