Can I use a Yongnuo RF 603N flash trigger with Nikon D3000?

Please suggest any other compatible remote trigger available in India.

You can use them for off-camera slave flash, but can't use them for RF triggering your camera's shutter as the D3000 has an IR remote, and the RF603 N and RF603N3 requires a camera with a cable remote.

Yes, you can use Yongnuo. In India, Sonia makes flash peanuts (optical flash triggers) that work by line of sight. You only need to wire one flash and the others can be made to fire almost instantaneously with these peanuts.