Question

1) Can activation energy be zero?

2) how activation energy is affected by rise in temperature?

Answer 1

1)Yes a reaction can have zero activation energy.Process with zero activation energy most commonly involve the combination of oppositively charged ions or the pairing up of electron in free radicals.For ex- dimerization of nitric oxide(NO2) to N2O4 which is an odd electron molecule have zero activation energy.
2)Activation energy is the “minimum energy which must be available to a chemical system with potential reactants to result in a chemical reaction” (basically the minimum energy for a reaction to take place), it is for that reason that temperature (which is a measure of kinetic energy) doesn't change the minimum energy needed but rather will bring you closer to the activation energy if you increase temperature and the opposite if you decrease it.