What is qualitative relationship between surge line, stage characteristic and throttle characteristic?
Since your question is divided in three parts, I do the same with my answer. First, however, we need to explain what the axes of the graph mean. The x-axis plots mass flow through the compressor, which is roughly equivalent to the tip speed of the compressor blades, and the y-axis shows the pressure ratio between entry and exit flow.

Throttle and compressor performance

The throttle regulates fuel flow, and this flow has to match the air flow. The limits are:


If fuel flow is too high: The combustion will create too much heat, so the turbine will be damaged.
If fuel flow is too low: Too little energy is added to sustain the current operating point. The engine will slow down.


If it is kept within those limits, the throttle will indirectly control the compressor speed and it's mass flow. More fuel flow will translate into higher turbine entry speeds, which will increase the torque produced by the turbine and speed it up. Since it is directly coupled with the compressor, it will see the same speed increase. This leads to higher mass flow and a lower fuel-to-air ratio in the combustor (relative to the state right after the throttle increase), such that a new equilibrium at a higher speed is established.

Throttle lines

For every pressure ratio the compressor will have a matching mass flow, and both move up and down in parallel. This is shown by the dashed lines. Depending on the blockage of flow in the turbine and the engine nozzle, different lines are shown for different grades of blockage. The solid stage characteristic line shows the limits within which the compressor will run, and a higher flow resistance narrows the range of speeds that are possible. The limits are determined by:


Lower limit: Here the compressor is run at the lowest possible speed for the given blockage, and the compressor blades run close to their maximum lift coefficient. When the blockage is increased, the flow over the compressor blades will stall and the pressure ratio will collapse.
Upper limit: Here the compressor blades run at high speed and a low lift coefficient. Running them any faster will not create enough pressure rise per stage, and again the blocking cannot be overcome.


Surge

Once the pressure rise per stage cannot be maintained (say, due to a stall of the flow over the compressor vanes), the high pressure air in the combustor will find it easier to escape at the front than to flow through the turbine and the nozzle. This leads to reverse flow and a sudden drop in combustor pressure, which in turn allows the compressor to reverse the flow and start pumping air back again. Now the pressure in the combustor rises again, until the whole process repeats.