Hello,
1. Yes, you can send via any shipping company but I would use FedEx. Having used FedEx for many years, I personally trust them the most. I got my processing done through a law firm in Canada and I sent my passports to them via FedEx. No issues at all. And yeah, I also lived in the US when I sent my passports to Canada.
2. You don't have to use Canada Post unless that's what the requirement is. While creating shipping label on FedEx website to send your passports, you can also create a post dated return label. You'll just have to change 'To' and 'From' fields and you are done. You can also go to any of the FedEx Kinko's for shipping labels but you'll have to fill out shipping form manually (using a pen). Any of the employees there will be able to help you though, should you have any questions. For the post date on return shipping label, you can choose any random date (2 months from the date of shipping, for example). It doesn't matter though as your return label will only become effective and you will only be charged once CIC returns your passport and FedEx scans your return shipping label. Make sure you include shipping box or envelope too along with return shipping label. Also, call FedEx and ask them if any other paperwork may also be required. Even though passports have no commercial value, a commercial invoice with zero value may still be required. People at Canadian border are very strict about paper work. If proper paper work is not included, your passport will get stuck at the customs. If FedEx tells you that no additional paper work is required, ask them to double check and tell them that one of your friends was asked to send commercial invoice with zero value because his passport got stuck at Canadian customs and then they will look into it carefully. A lot of FedEx employees are not aware of this important requirement so challenge them if they tell you otherwise. It's not just FedEx, you'll run into the same challenge with UPS or any other shipping company too but FedEx goes above and beyond to help their customers if there is any problem.
3. You can put "Citizenship & Immigration Canada" in both company name and contact name fields. If you could share the complete address you have to send package to, I can tell you more specifically. For the return label, obviously you'll put your own first name and last name.
4. Yes, you can use any service. I would avoid DHL though as they have a very bad reputation. Use FedEx or UPS. As I stated above, I personally like FedEx. But choice is yours.
Good luck!!