i thought almost any action based mmo allows you to attack while moving?
action based mmos: Tera, Vindictus, C9, Dragon Nest, Blade & Soul, Darkfall2 etc etc there are so many.
Personally, i dont like action based mmos because pvp becomes dependent on how free of lag your connection is. The player with the least lag will usually wins. Bit pointless to me.
If you like action combat i could suggest u look at single player large scale action games: Any of the Dynasty Warriors series 1-4 (u need to use an emulator to run these but they are magnificient action games). Dynasty Warriors 5 runs on PC. A huge action game, better than Tera afaik.
Be warned - I am a major player of Regnum Online the mmo. I've been playing it for about 2 years and rarely go without logging in at least once a day. You can also look at good alternatives to Regnum such ase Aion online and Aika Online.
I often strafe or backup while in combat.
All ranged weapons allow this.
Even melee weapons allow you to move but the short range prevents much more thqn just circling the creature.
Healing strength is diminished while moving.
Some mindforce (scifi magic) fails or resets if moving or hit.