Is global warming linear in the sense that doubling the emission of Greenhouse gases will result in a doubling of global warming. Is there a threshold, i.e. is there are certain concentration of GHG where global warming is triggered and additional gases do not lead to a faster global warming?
No. Consider water vapor. Water vapor is a greenhouse gas. As the temperature increases, more water is evaporated. Since water vapor is a greenhouse gas, the temperature will increase. Clouds, however, form from water vapor, reflect sunlight.
The earth is not as linear as people would like.
No, it is logarithmic. Each doubling of CO2 concentration will result in a constant increase in temperature which is called the equilibrium climate sensitivity, estimated to be 1.5C to 4.5C. Wikipedia.