It does absolutely not make sense timing bringing up capacity online. The most optimal strategy is to mine as soon as possible. A mined block is worth more than the loss resulting from difficulty increase of one's mining in the next round.
That would depend on how much computing power you were going to bring online and how long till the next difficulty increase.
No, it's not unless we are talking about some crazy scenarios that someone increases the difficulty by so much (say 20-fold) that next round mining brings less income than electricity.
Each block you mine in the round n will lower your mining output by 1/2016*(your_hash_speed_next_round/global_hash_speed_next_round)*2016=(your_hash_speed_next_round/global_hash_speed_next_round) in round n+1 due to difficulty increase resulting from getting this particular block sooner. And this number is always less than 1 because your hash speed is lower than the global hash speed. So it is always (without taking into account electricity costs) worth mining a block without worrying about the next difficulty increase.
In a less abstract example, suppose, you have 10% of the total capacity. You bring it online just after the difficulty increase. You mine 10% of 2016 = 201.6 blocks.Suppose you could have entered online sooner, at 80% of the previous round where you had 13% of the capacity. You mine 0.13*0.2*2016=52.4 blocks. It increases the difficulty by extra 2016/(2016-52.4)=2.7%. You mine next round 201.6/1.027=196.3 instead of 201.6. Net gain of 52.4-(201.6-196.3)=47.1 blocks.
