In the advanced Campaign the Chaos Beast gets 4 dice for choice. May the Chaos Beast take 1 X die and 3 green ones (or 3 yellow ones), while there are only 2 dies included in the game or is he only allowed to throw 2 green and 1 yellow die?

AoD rules, pg. 9:

For each morph die (indicated by a
die icon with a question mark) the monster has on its
reference card, the overlord player may choose a red,
white, blue, yellow, or green die to roll, as limited by the
dice that came with the game.

Does this mean, the diamond upgrade is useless (just the dice part) because there are only 2 green dies, so the third die has to be yellow - as it is on gold level? Or should there be more than 2 green dies?

Why should it be useless? You are free in your choice of dice with Diamond CBs, so you may roll red-white-green-green (possibly coupled with an Aim), if you really need a high damage roll. This is not possible for a Gold CB, with one die fixed as yellow.

funmasta said:

You are limited to the dice that come with the game, but you are not limited to green and yellow.  You can choose from red, blue and/or white as well (though if you have more than one of these you must declare which attack type it is before rolling.)

If i roll red, white and anything else does only the one i declare as melee or magic attack have a miss on a X or do i miss if one of those 2 misses?

Any rolled X is a miss. That´s why you´ll probably want to Aim such an attack.