Let's see...
1. There are methods, if you have wifi the easiest method is PokéCheck: http://pokecheck.kraftpaper.org/
2. The egg would be perfectly fine, legality wise.
3. No, they can't if the parent isn't on the game (they still wouldn't be able to distinguish it from a hacked one if you do it correctly).
4. I highly doubt this, but I can't rule it out completely.