I don't know the pest you are seeing but how about drenching the soil with insecticidal soap solution and then repeating every week until they are wiped out? Am I seeing this plant positioned in the middle of a room with no light? You'll have to go into more detail as to how you are growing this TREE before I can give advice about lighting.
These trees have tree-like root systems, so they need adequate pot size so that there is enough growing media to support the root expanse. Otherwise, the roots become root-bound and watering will simply not supply the constant moisture that these tree flourish with.
The leaf damage can me old and can be due to a lot of causes. Underwatering, low humidity, trauma, amoung many other factors can cause leaf damage. Since these leaves are so large, everything that can cause leaf deterioration is magnified.
