I believe doubling the cycle time also halves construction speed, but don't quote me on that.
1. HAH! I'll quote you if I want, because I'm anarchistic like that.
2. It doesn't, as most construction/production/research etc. is calculated based on the number of seconds since the last production cycle. (Otherwise, advancing time 30 days would result in 1/6th of the proper growth.) Note, however, that some things (like officer skill increases and communication checks) do grow more slowly with longer cycles, due to Steve not working out all the math for the proper exponential formula.
2a. Also, in the areas where you can't queue production (Ground Force Training is the first to come to mind) your overall build rate will be slower due to extended 'dead time' between items.
2b. Due to the 'calculated by seconds' factor mentioned above, going to a very short construction cycle (an hour, say) can cause your progress to get rounded down to 0, and you end up not making any progress unless you advance time by a day or so.