Moas can only lay eggs of the same color they are. Therefore, Blue Moas will drop Only Blue eggs, White moas drop White Eggs and Black Moas drop Black eggs.
Those "Random Ambrosium Shards" Might be there for two reasons:
1st, You might be using a Holystone tier tool, which have a random chance to drop Ambrosium Shards. as of why those are bugging, I have no idea.
2nd, This is the most probable one: there is a random bug happening out there that makes the character "pop" Ambrosium shards when walking or doing something. Those are Phantom items and will give you nothing. Therefore, just ignore those and remember, this is the Alpha Version, so there will be many bugs ;D
About the 2nd Bug, everyone is having that bug at the moment. Its probably due to an error on the script that is suposed to say "Conquered" when you have already completed the dungeon, and not allow you to enter on it again. The game recognizes you have completed the dungeon, but the script to say "Conquered" won't load and, therefore, it will stay as "Available". When you restart the Java (used to open minecraft) the scripts of the game are also restarted. Most of 'em come back the way they were before, as it is suposed to be, but some seems to be reseting completely and, therefore, erasing any data you sent before. Althought it says "Available" you Cannot enter the Dungeon because it as already Conquered before by the player, but the game won't recognize.
In Resume, The Script to say "Conquered" Is probably broken (missing a "connection" to the main script") and it just shows the wrong title for the dungeon. You Won't be able to re-join it as it was already completed before.