Harm spell

Easy one here, does the Harm spell have the attack trait?

Also can I cast Harm (touch range) while wielding a greatsword?

It does not have the attack trait, and you can cast it while wielding a greatsword. The one-action version's only component is somatic, which has the associated rules:

"A somatic component is a specific hand movement or gesture that generates a magical nexus. The spell gains the manipulate trait and requires you to make gestures. You can use this component while holding something in your hand, but not if you are restrained or otherwise unable to gesture freely.

Spells that require you to touch the target require a somatic component. You can do so while holding something as long as part of your hand is able to touch the target (even if it’s through a glove or gauntlet)."

To add an additional note on this, touch Harm doesn't even involve an attack roll anymore. The target makes a saving throw against it instead. Which is usually good because they're almost certain to take at least half damage and great because multiple attack penalty is not involved.