Just a quick response here,
A 'PAN' call is a situation of URGENCY whereby a condition concerning the safety of an aircraft or of some person on board (or within sight) exists. However, the situation does not require immediate assistance
A 'MAYDAY' call is a situation of DISTRESS whereby the condition of the aicraft is being threatened by serious and/or imminent damger which requires immediate assistance.
The 'Heavy' part of a callsign (which comes at the end, e.g. United 256 Heavy) signifies that the aircraft comes under the wake turbulence category of 'heavy' rather than 'medium' or 'light'. This allows the controller to quickly know the limitations as to how much separation is needed between aircraft. 'Heavy' aircraft are those like the A300/A310, 747s, Most 767s, etc... The number of engines is not taken into account, just the MTOW.
Finally, as far as I am aware, the 'Heavy' callsign extension is only used in the USA. If anyone knows of anywhere else it is used I'd be interested to know, but for our airline's operations we use it only in US Airspace.