Yes, CIC has been sending us letters via email - the sender is "CPCS Client Notification / Notification du client CTSD (IRCC)."
My wife and I are both women, so no husband here

Our checklist did not include the police check (we are also using an immigration consultant who did not have me get one yet), but it seems possible CIC might request it during the process.
If your husband is in Canada on a tourist visa and you submitted outland, he must maintain valid visitor status. At least 30 days before his status expires, he needs to file for an extension, and then he can stay ("implied status") until he gets notified of his visa extension status.