On top of this order, creatures and weapons with ability will attack first and then "activates" their ability. E.g: A Vampire will do the damage first and then heal you afterwards. Though this doesn't matter most of the time.
Although that holds for the ability Vampire (and many of other abilities), I'm afraid that it is not the case in general. Actually, some of creatures' abilities, as well as all of their statuses, are applied before their attack. For example, the ability Acceleration/Overdrive is applied before a creature's attack so that it deals more damage. Also, the passive ability Swarm which Scarabs have is also applied before each Scarab's attack, so a newly played Scarab does not bypass Gravity Shield.
For creatures' statuses it is natural to think so; one notable thing is that poison counters are also applied before attack. Thus a creature with 6 HP and 2 poison counters on it will bypass Gravity Shield, since the poison counters reduce its HP to 4 (under threshold) before its attack.
Ah yes, that's true. Totally forgot about acceleration. I didn't say anything about passive ability (or passive skill or whatever the name is) and status because I feel those are entirely different and didn't think it was necessary because it can get a lot more complicated.
With that said, I think it'll be interesting if the attack vs ability/skill/passive/status orders will be revealed somehow.