for me, I will go for yes to 2, 3 and 4.
Reasons behind answers:
Technically, it would be better if you have no chiller = higher temperature = higher metabolic/growth rate for bacteria, no skimmer and removers = higher levels of nutrient levels for bacteria. However, once we start to use them, the temperature reduces, stressing and killing off some of the bacteria. With lower nutrient, bacterial population starts to die off rapidly. The dead bacteria population may cause a mini nutrient spike. Hence, my preference of cycling a tank with parameters as close to normal situation as possible.
As for 1, it depends on how you handle them. I rarely hear people acclimatizing the rocks with dripping method. You should expect some of the population to die off, however, with that said, the population should rebound fairly quickly. Coraline algae can produce spores when stressed, not much of a problem as it should recover slowly if anything were to happen. As for ending up with shortening of cycling period, I do not believe in cycling periods. As long as there's a reasonable population of bacteria around, it should be fine. Our tanks are cycling every single minute, when bacteria population dying and growing according to nutrient levels. I would recommend a cycling period for sterile tanks though as there is no bacteria population to speak of in the first place.
If your system is unable to handle bioload introduction shortly, I would say your filtration is rather insufficient. For me, I will oversize the filtration to the level where even if the bacteria population suddenly gets wiped off, it can still sustain the bioload.