1. Yes the lit provides an external energy for the reaction to reach its activation energy, however, there must be another source of energy to keep it from burning.(hint: look at the main composition of natural gas and part 2)
2. That is because products of combustion of methane(CO2 &H2O) are more energetically stable than the reactants. So in a sense, reactants are relatively less stable, so the bonds are easier to be break, therefore energy absorbed is lesser. Whereas, products are relatively more stable, so their bonds are easier to formed, therefore more energy is released. Hence, overall is always an exothermic process.
3. This is probably due to the nature of exponetial graph. Do you know about Arrhenius' equation?