In you response to your questions.. that's a tough one.
When to call is tough, because some programs rank right then and there..
It depends on the relationship fo whomever is calling on your behalf and the person they are calling. If they have a good relationship with someone there, I would have them call. Otherwise, I would say that you should have them call afterwards. Best bang for your buck. A lot of times after the ranking is done, PD's will change ranks based on a variety of things..including a phone call. Your biggest bang for when there is a personal connection is beforehand, in my opinion, but those programs should be for ones that you really want to goto.. so that way they can send an email on your behalf, and say.. hey, this dude is really into your program, and he's a good kid FYI. Then they will take a close look at you while you're there,...and if they have more questions, they will call to find out more. Generally this tactic is employed BEFORE you get the interview.
It is very helpful for the letter writer to have their number in there to say 'call if you have any questions'. My understanding was that a bunch of people called on my behalf asking what they thought of me. This all happened AFTER the interview.