Can I bring a satellite phone onboard a plane? [for rescue purpose in case the plane crashes]?

You can bring it. The chance of your needing it for the stated purpose is beyond remote. And if you did, it likely wouldn't work anyway.

Yes, you can bring it, but you can't have it turned on while flying.
Most crashes happen during takeoff and landing. If you were in a condition to use it, you could just as easily walk back to the airport. In the extremely off chance that something goes wrong mid-flight, you will probably be too dead to use it. Even if you were in one of the extremely small number of mid-flight crashes in a remote area where people survive, unless you have it in your pocket, you probably won't even be able to find it.

yes but chances are slim that the plane would have a survivable crash is slim. Also, if the plane crashed into the ocean and people survived, the rafts have beacons and flares and chances are your phone would be waterlogged or damaged or even lost.

Not if you're flying into India or any of the other countries where it's banned. You don't need a satellite phone in case it crashes - unless the aircraft crashes in a remote uninhabited area/ocean, search and rescue teams are able to trace the last known position or the approximate location. In any case, if the aircraft crashed and you were able to evacuate safely, you wouldn't be allowed to take anything with you while evacuating.