1. Is there any requirement for a specific type of wire to support a lay in "troffer" style fixture in suspended ceiling systems?
2. Can the fixture support wires be attached to the eye lags or bolts that support the ceiling system or must they have their own anchors?
3. Are there clips that accomplish this support and negate the need for wire support?
1) Not to my knowledge
2) I would think so, however the lags may not be mfg rated for more weight than what they are already carrying
3) If you are thinking about clipping the troughs to the grid for support, in most cases the grid is not rated to support anything except itself. You can use clips; 410.36*.
If the deck is wayy above the drop ceiling, you can use an extension tool to shoot in (assuming it's a concrete deck) clips with your own tie-wires.
You're asking more about local building codes than NEC. There are two questions: 1) is the grid a fire barrier or not and 2) is it mfg rated to support lights. Even if it isnt a fire barrier and is mfg rated to support luminaires, local codes may require you to independently support all of your troffers.
*I've read some FDs do not want the troffers clipped to the grid, reason being if they have to tear it out with a fire axe, the troffers dont come down with the grid. this is also why anywhere Ive worked the lights have to be independently supported regardless of the grid type.