Confusing, huh? Some thoughts:
1) Each part of the drive train has a limit, and sometimes you hit one first before another (the first limit calculator in the EC products is a nice way to work thru this!) so transmission limits are expressed as if not connected to engines, although they are obviously directly related. Also, these limits might be different, so you have to have three eyes, one for transmission torque, one for engine torque and one for trees.
2) SHP is actualy not a limit (no gauge reads it and no test runs at it), it can be a rating (which pilots don't need to care about). SHP is however the power that is produced by a torque (which is a limit) times an rpm (also a limit). Just like horsepower is also a force times a velocity, or a weight lifted at a speed, torque time rpm is horsepower (or kilowatts). The engine/transmission system is running together, and it all "feels" the same torque (unless you are in a 222, where the mast torque is also a limit!)
3) Torque is the twisting force applied to the gearboxes, and is the thing that breaks gears. Gearboxes are often qualified without putting in any power, they just apply a twisting force to the gearbox and then spin it at the required rpm. The actual power used to qualify a gearbox might be 10% of its rated power, when the box is tested by torquing the input and then spinning the box.
4) "how, for example, can you have more than 100% of anything" Pilots aren't always Einstein, so it is easier to just set an arbitrary torque or speed as 100%, and then test to see how strong the box is. If it can take 10% more than that 100% we say it has a limit of 110%. Still don't understand? How can you get a 10% raise? Be sure and tell your boss it is impossible to get more than 100% of your salary, and give the 10% back.
5)"how can engine or transmission SHP be used to calculate either TQ or NR?"Great question, the calculation is torque in ft-lbs times the rpm in revolutions per second times 2xPi = the power (in Ft-lbs/second). Divide by 550 to get Horsepower. Actually, you find out from someone who knows what is the horsepower for 100% torque at 100% rotor and then ratio to find actual horsepower. For example, in the Black Hawk, 100% torque is 2828 HP at 100% Nr. Therefore, at 66% torque and 100% Nr, the helo is eating .66 x 2828 = 1,866 HP. At 66% torque and 105% Nr, the aircraft is eating .66 x 1.05 x 2828 = 1,959 HP.
6) "What does engine PPI 105% mean?"The term is British usage, and in the US it is said to be "above spec" by 5%, thus PPI of 105% means the engine produces 5% more power than the minumum expected for that type, thus the helo will climb a bit faster and carry a bit more under engine limited circumstances (and NO more under conditions where the transmission is the limit).
7) "Can engine SHP be used to calculate transmission limits?" The transmission is limited by torque, since that is the gauge you are given. To compute HP from that torque see 5 above! A note: Engines are usually more powerful than transmissions, because engines lose power as temperature or altitude are gained, so the designer buys a bigger engine and lets the transmission reach the first limit, up to a few thousand feet of climb. This means the helo will carry its full MGW on a hotter day and a higher altitude, a nice thing. The Black Hawk, for example, doesn't see an engine limit until perhaps 4 or 5000 feet on a hot day.