1. Nope, my phone isn't rooted.
2. As far as I know, I'm not doing anything at the time of reboot. The first time I was suspicious is that I found the phone to be loading weatherbug (I leave it showing the temp in the notification bar) when I woke up for work earlier this week, and when I held the home button, it didn't show a full six apps as having been recently used. Tonight, the phone was on the charger (about the only thing in common with the first apparent reboot) while I was playing video games (PS3, not on the Droid), and noticed the Moto logo showing from when the phone first boots up.
3. Here's a list of my apps:
Contacts GroupU
Quick Settings
Backup
TV.com
Meridian
Multimedia station
TaskManager
WeatherBug
Grocery King
ACast
CadreBible
eReader
Facebook
Timeriffic
Corporate Calendar
Documents To Go
FlightStats Lite
More Icons Free Widget
SportsTap
SoxNews
Handcent SMS
System
ShapeWriter keyboard
S2 Calendar Widget(D)
Quickoffice
App Referrer
Tapatalk Pro
Shazam
EasyMoney
Keeper
Documents To Go Full Version Key
Camera
Barcode Scanner
Listables!
MessageNow
ASTRO
Twidroid
Note Everything
Ring Toggle
HandyCards
Astrid
ShopSavvy
RingGuard
(edit for clarification)