In my opinion email is better because it's faster and there is less risk to loose important papers.
CIC contacts the sponsor for the first part ( sponsor approval), and then the applicant for the second part (stage 2 in the visa office). After you get the sponsorship approval, you will have a file number that allows you to check on progresses on ecas - online system. Ecas is not very reliable and doesn't provide much information, but you can check it to see if anything is happening.
If you are from a visa-exempt country, then CIC might not request a passport, and not even the copy. It depends on the VO. If the VO requests the passport, the request will be sent ( generally by email) to the applicant, unless the sponsor is listed as a representative, in that case everything goes to the sponsor.
Good luck,
Sweden