what is the function of 1. laod loop drop and 2. synchronizing droop in power generators?

Answer 1

Speed droop is the speed variation from full load to no load.

Speed droop in a generator allows multiple generators to share the electrical load in a stable fashon. Speed droop is applied to the governor of the prime mover as a means of modifying the speed setting(set point) of the governor based on the amount of work it is doing. If its not doing enough the prime mover is sped up a little more to take additional load. If too much work is being done the prime mover is allowed to slow down.

With generators operated in parallel they all run at the same speed due to the electromotive forces in the generator coils. The load is distributed between the generators by how much power the prime movers supply to turn their respective generators.

Governors on prime movers control how fast a prime mover(engine) spins. As the engine slows down the governor adds fuel to speed up the engine, if it goes to fast it reduces fuel to the engine to slow it down.

When a generator is placed on a buss its speed will change to match those already on the buss. If this speed change causes the generator to speed up the governor will see this speed increase and remove fuel in an attempt to slow the generator back down. The engine ends up doing less work and therfore produces less energy. As less energy is produces electromotive force is reduced further allowing the generator to speed up and the governor pulling back further.
This is a downward spiral which if left un corrected would allow the generator to just spin without supplying any current and in an extream case would allow the generator to become motorized. (Motorized mean that electric power from the buss drive the generator like a big motor) ... The above also has the opposite situation where the governor continues to increase speed and takes extra load from the buss as it slows down. In either case its a run away condition.

An operator would have to manually adjust the governor to cause the generator to do more or less work and maintain its share of the load.

Speed droop is what automatically adjusts the governor to prevent this runaway condition.
Speed droop is a type of feed back that is applied to the governors speed set point. As more load is taken by the generator speed droop will allow the governor to operate at a reduced speed setting. This prevents the generator from taking too much load. And as the generator gives up load the speed droop will increase the governors speed setting