Do Evolutions combine, for example Breath of Doom, Mecha Blast, and Claws of Steel?
If not specifically stated as with Breath of Doom, the term deal X damage always translates to


  Deal X damage to all target monsters and each monster that has taken damage from you this turn.


If you're in Tokyo, this means your target is all monsters outside of it. If you are attacking Tokyo, your target is all monster inside of Tokyo (Bay included). In case you have dealt damage to monsters that are not your target, they will also take extra damage from these modifiers.

And vice versa, the translation of "you dealt X or more damage" is


  All of the monsters that you targeted have taken X or more damage originating from your number of rolled claws, damage from cards and damage from power-ups.


So, if you're in Tokyo, you need to have at least dealt X damage to all monsters outside of Tokyo. This can be important because there are cards that affect only your neighbours.

This is how the total damage is counted after each effect in your example:


You roll a single claw.


  Total DMG: 1: Only the monsters in Tokyo are affected

Use Breath of Doom.


  Total DMG: 1: because the only monsters affected by Breath of Doom are the ones outside of Tokyo, hence not your target

Use Mecha Blast.


  Total DMG: 3: At this point you've already attacked all other monsters, so all other monsters take extra damage. In case you wouldn't have played Breath of Doom, only the monster(s) in Tokyo would have taken 2 damage!

Play Claws of Steel.


  Total DMG: 4: The same reasoning as in the previous step.