In Canada, you must also be a Canadian tax resident working for a Canadian entity is all that matters and only 10% of your R&D work may be outside the country. It does not matter where you work exactly. The rule are different in other countries.
Yes, you will. Be sure you calculate your office space as a percentage of your total home square footage. You need to be sure you also use your office space only for work. I have had clients and friends who have had "surprise" IRS audits to verify that the home office was really only used for work.
Your personal tax return doesn't need to list your business' mailing address, so they won't question the difference in mailing vs. physical address.