For all that's known, Grievous was a pretty good fighter before he got turned into that machine monster. So, like Vader, he is still alive in a Force sense.
I guess this is also why his MagnaGuards don't carry lightsabers, but electrostaffs instead.
Nobody cares about Grievous. He's part of the later, shittier movies from a different director (yeah Lucas in 2000s has nothing to do with the Lucas in the 70s).
Yep, he picked it up and just turned it on. I guess you could say it was natural instinct but I would have to think such a thing would require a great deal of concentration.
Plus there's the fact it's quite canon that there's a power source. Luke bought one when he built his second lightsaber.
EDIT: Thanks to Wookiepedia I now see that the earliest lightsabers were the result of the user channeling the force through the device. Later to be changed to various power sources which resulted in superior weapons.