For example, when a Mega Altaria is going to mega evolve, does in the first turn stay Dragon/Flying or Dragon/Fairy? Because I think the stats only change after the end of first turn when mega-evolving.
I would like to know if in the same turn Altaria is mega-evolving and a dragon move would hit him or a ice-type would make x4 damage..
Only the Speed stat changes on the second turn. I just tested it.
Here is the game where it mega evolves, and here is the game where he didn't mega evolve.
As you can see, he took a lot less damage when he evolved, so it does change on the first turn.
Only turn-order is unaffected on the turn of Mega Evolution. Because the movement order is determined before any moves are selected, then even if the Pokémon Mega Evolves the movement order will still play of as normal. This goes for Mega Abilities that affect priority, so if a Pokémon gains Prankster upon Mega Evolution it will not take effect until the second turn. So any change in typing changes on the turn a Pokémon Mega Evolves, along with all other stats.