1. AFAIK, you must apply in person at a mission abroad to get a passport issued, it cannot be done by mail.
2. Some missions do not want people picking up their passports or cards when they come in and have courier arrangements. They will generally only allow to be sent in that country or consular area.
3. Personal experiences/knowledge of last few weeks. I knew someone traveling from LA to Europe, who went the Emergency route, got an emergency appointment next day in LA, and had their passport 4 hours later.
3. GU's assessment of 8 day average in EU is spot on and has as much to do when "pouches" go out as anything else (i.e. if the US Embassy in Brussels gets its pouch sent on Tuesdays and your application is in the system on Monday, you might very well have it back in Brussels on Thursday or Friday, if it goes in on Tuesday and misses the cut off time, it may not get back to the Embassy until the next Tuesday, and sent to you on Wednesday or Thursday.)