In a 3-pin socket there are 3 wires: phase, neutral and ground. Neutral is taken out and grounded and earth wire is also taken out and grounded. Is it possible to short the neutral and earth terminals and then grounded?
That's horrible. Neutral and Equipment Safety Earthing (in mains electrical service, ground) must not be crossed, bridged, shorted, or biased. They must remain completely separate, (except in one specific place defined by your Electrical Code, which is a place you will never be unless you are installing main electrical service.)
Noting that you came over from the Electronics stack, we are changing terminology on you. In low-voltage DC electronics, "ground" is the normal current return: Vss. In mains electrical, the normal current return is called neutral.
The equipment safety grounding system is only there to take accidental shocks that would otherwise shock a human or start a fire. For instance, if a frayed wire contacts the metal chassis of a machine, instead of energizing the chassis and killing the next human who touches it, massive current will be carried back to source, causing the overcurrent breaker will trip. Current should never flow on it unless something has failed.
If you dislike this safety-ground feature, or do not understand it, or do not want to use it properly, then don't use it at all. Use a 2-wire cord to a 2-prong plug. You may find that the western listing agencies, UL, TUV, CSA etc., have some extra requirements for your product, e.g. double-insulation.
Why not short neutral and ground locally?
What happens if a neutral wire breaks upstream? Everything else downstream of the wire break is trying to return current via neutral. So all that current from all those machines travels the neutral wire to your illegal short, hops to ground, and takes ground back to the main panel, via the official neutral-ground bond, back to source. This means many amperes of current are coming through your little plug. Neutrals don't have fuses, so this burns your house down.
What if a ground wire breaks upstream? Normally if a neutral wire breaks, current can no longer return to source, and this has the effect of "floating" the neutral wire at line voltage. If you have also bridged it to ground, now you are also floating the grounding system at line voltage, at least on your machine. Anybody who comes in contact with that gets shocked.
What if both neutral and ground take a hit? Similarly what if all wires are cut, and the machine has capacitors, or inductive kickback as it spins down? Again neutral floats up toward line voltage which the system would be able to handle normally. Your bootleg bonding means ground floats too, and shocks people.
is it possible to short the neutral and earth terminals and then grounded?
In the US, the electrical codes only permit the connection of the earth and neutral connections at one place in a building. This is called the "bonding point" and it's important that it be done correctly, because it's critical to the safety of the installation.
Why only one place? Several reasons. One big one is fire protection. The bonding connection really does have to be done right so that it can carry large currents when some fault connects hot and ground. Another ground-neutral connection that's not as good can start a fire if it tries to carry those large currents during a fault.