Looking at posts in this community, people have received PR cards in 2 weeks so that seems to be the current timeline.
At the airport. However, if you mention you are doing soft landing, the officers might not apply for the card right away and might ask you to apply when you move permanently. I think in this case, you will need to apply it online. This is from what I have read so may be someone who has been through it can confirm or deny.
Again, from what I have read you would need to give a local address but I think people have been able to use UPS mailboxes.
Not sure about this one.