JoAnn Fleming Owner at Fleming & Associates CPA, PC

yes. As long as your main place of work is your home/office.

You will have to report it on your personal tax return on Schedule C. If you deposited it into your S corporation bank account, it will be counted as income twice. You can expense it on your Schedule C and net to -0- since it included in your corporation income.
In the future, provide your S corporation name and federal ID# to insure that the income will be reported as corporation income rather than personal income.

I don't think it matters, but check with the bank.

The income tax you pay will be based upon the net profits of your business. The profit or loss will be taxed on your personal tax return. In addition to income tax, you will be subject to self-employment taxes.
Depending on the amount of tax that you will be have to pay, you may be subject to paying estimated taxes on a quarterly basis during the tax year, rather than just paying 100% of your taxes when you file your income tax return on April 15.

You can take a credit in Canada for foreign taxes paid in the US. You should not pay tax twice on the same income.
Is the product or service you are selling subject to sales tax? You have to provide more info to determine that tax.