Erm... Not that sure regarding the eggs.

Regarding the two bugs, firstly are you using a holystone axe? Oh and does this happen to every tree or just specific ones?(Golden Oak, Skyroot, for example.)

Lastly I think you don't need to care much about the dungeon bug. If you've already conquered it then all's fine, it's not like you would get lost and actually try to enter that same dungeon again anyways.

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.

Ok, that will explain some things, but about the "RANDOM" dropping ambrosium shards: yes im using holystone tools, who  will use their zenite tools for nothing, however, the random drops i have are from ANY type of wood, and the new fancy log wall, BUT sometimes i CAN get the drops from the wooden stuff, and sometimes i CANT. However i ALWAYS get the ambrosium drops from holystone

and i have another question; so about these wild moas that spawn in the night, do they drop ALL type of moa eggs? i have been watching one wild moa for a chance to get an egg, but NO the moa decited to TROLL me and despawner:(

Well then it could be the phantom drop Macro has already said...

Half of those random shards are phantom and another half of them are from your Holystone Axe. Should explain why you can only take some up and not all of them.

By "wild moas", do you mean cockatrices? If you do not know what they are, try walking up to them and see if they start shooting you with poison darts. If they do, their cockatrices and from what I know their just a hostile mob. They shouldn't drop any eggs.

whell i spend some time in the wiki and i read that Cocktarices may lay moa eggs, however i dont know do they lay ALL type of eggs or not?

I'm fairly sure Cockatrices(Aggressive) do not lay Moa eggs. If anything, it should be Moas(Passive mobs) that lay eggs.

They both look alike but their definately different.

Please relate to this Article

Cockatrices will only drop Feather, and that is when they die. The ones you are refering to are Wild Moas that are found, obviously, in the wild (any random part of the Aether). Those do, yes, drop eggs but only the ones from their respective color