You can fertilizer any time you want. Before or after. And yes, the fertilizer stays in that spot even if there are no crops there.
And I think it takes a month for a spot of land to degrade by 1 soil quality, so if you put 4 fertilizers on the spot, making it maximum quality soil (dark brown), then it will only lose 1 soil quality after a month. (Although, I'm not completely sure about that...)
Also, fertlizers don't seem to make better crops they just make stuff grow faster. But since it lasts for so long and you can harvest sooner, it's definitely worth fertilizing your land....
Supposedly a spot degrades one level every two weeks or so if you have crops growing there continously, so you can use decent fertilizer to replenish (supposedly: I haven't finished testing it myself yet). Also a major factor on how well crops grow is weeds: make sure you don't let weeds grow near your crops, it is alright if they're all the way on the other side of the field, but anything adjacent is bad for crop quality and should be sickled as soon as they sprout.