1. I believe the Invaders World Settings toggle (in the Settings tab) works without regen; it simply flips the [INVADERS:YES] tag in d_init.txt to :NO]. This should work without regen given that is true for temperature, caveins, and weather. Toggling specific races from Civilizations or Other Creatures tab would definitely require a regen.
2. Near as I can tell, the presence of non-water rain disables accumulation in murky pools completely. I don't think there are any examples of good-biome rain in vanilla, but under
Surroundings, evil rain is mentioned to have this effect. Since the different flavours function the same, mechanically speaking, I expect the same is true of good rain. Furthermore, even if it did it wouldn't really be a drinkable substance... Drinks are derived from the raws of a plant, the biome rains are just an inorganic material with a liquid form (and attached syndrome).
That said, the good rains do have an effect: beer rain will temporarily add the NO_DRINK tag to a creature, while milk-and-honey rain will add the NO_EAT tag. These will apply if the creature inhales the substance, and given the substance's boiling point, this should happen as soon as it lands on anything (because its boiling point is 895 units lower than the freezing point of most everything else). Even so, use of good rain in this way may not be advisable, as it prevents the ability of your creatures from eating or drinking and gaining happy thoughts in this way. (This may or may not even be a problem depending on how well your fort is doing.)
3. Looks like they have a 25% chance of laying a normal egg (the other 3/4 of the time being limestome, marble, or dolomite). Set up a stone stockpile to take these boulders (ensure there is always space) and disable boulder crab eggs in your food stockpile and your kitchen menu. This should remove any non-egg boulders from a nest box as soon as a hauler as the opportunity, while leaving eggs to mature. Eggs aren't directly edible in masterwork so even hungry dwarves should leave them alone.
4. ./shrug Be patient I guess. I'm not familiar with how to game the caravans, but you can try to make the trip more profitable by selling goods that are a lot more valuable than what you're buying. In theory that will make future caravans bring more stuff. It might also require some gaming involving caravan weight but I'm not familiar with that.
