T2 has nothing to do with the actual peening cycle time. It is only used to determine intensity.
1. No, it is not necessary since your peening intensity is already established. Leaving the parts in longer (or even shorter) periods affects coverage but not intensity. Intensity is determined by shot size, hardness, velocity etc. but not exposure time.
2. Again, there is no relationship. To achieve 100% coverage you determine how long it take to make enough dents for 98%. Then for 200% coverage you go twice that time. Did you notice I never said anything about T1 and T2? They have nothing to do with setting your blasting time.
3. See above. If you had instead asked if we peen for more than 200% the answer would be yes you could possibly cause damage or reduction of fatigue life, depending on the particular material and how much over 200% exposure you endured.