Not true. As long as your ballasts are capable of 240V, the cord doesn't matter. Just make sure your ballast is 120/240 or has a switch to set it to 240V before you try to go that route.
That's a big risk in my opinion. There will be people through here that do it, but unless you're the kind of person who seriously pays attention the the details,i'm of the opinion that buying pot is cheaper than paying a lawyer.
If your controller is wired for 120V you ca't get 240V out. I wouldn't want to venture a guess at what you would need to do to wire up to 240V without looking at the wiring diagram for the controller, but I'm sure its possible to do it as long as the controller is capable.
Some ballasts will...
I saw that one too. I was tripping balls on good microdot acid. When those light pods stretched out over the front row, my buzz went into turbo mode.
And here's one of my AC/DC favs.
Serious Seeds.
They were the originators. From the pack that I grew out to get my mother, they were all pretty similar and stable. The one I settled on was a stand out among them and I've since made S1 seeds that are also very stable.
If you end up doing any research you will see pretty good...
I'll second the Kali Mist suggestion. I've been growing KM for 6 or 8 years now and I can definitely vouch for the reputation the strain has. I feel fairly certain it would fit your needs.
If you click on the link you provided and pull down to the specs, you'll see that the relays have a 120v control circuit. That's why the neutral is called for. Definitely go with the 3 wire plus ground.