1) I already said that they wouldn't.
2) Obviously yes
Then, serfs and Inns would become obvious hogs: every building would be in a faster-time environment for every purpose, but ones further away from the Inn would get much more off-time while the civilian goes there and eats; also, you'd need more serfs in order to manage the production surplus or else the production bonus would be in vain - but this is only a minor problem.
A bigger problem is that when players with equal skill play against each other, the first to attack would be the one to lose the game, since the other one can use the time needed for the enemy to come near to train more troops; making this time more effective by boosting production without making troop movement faster would also make turtling strategies even more effective, and I'm pretty sure you don't want that.
Last but not least, it would make feeding your troops even less feasible, since the time your serfs spend bringing the needed food would be more damaging to your economy than usual.
These problems are overcome with the increased game speeds simply because units, both civilian and military, move faster.
I don't think it to be a bad idea per se, mind you, but the fact that you can already specify different game speeds for peacetime and post-peacetime in my opinion does the very thing ("You could have "large bases" with 5 woodcutters, 2 sawmills, 4 farms, etc. which would result in much faster gameplay. However, unit movement would be the same, so micro would still be reasonable.") you proposed this for, but better.
Sorry: I don't like bashing ideas, but I think this one would not work better than what we already have.
Just when you think you know something, you have to look at it in another way, even though it may seem silly or wrong. You must try! - John Keating, "Dead Poets Society"