When a village's farm is reduced to a level where is doesn't have enough capacity to support the current population of the village, then you will not be able to queue any upgrades or train any more troops until you either reduce the population of the village (by killing troops or demolishing buildings), or upgrade the farm. Your troops will not automatically die when your farm is catapulted. Note that the farm cannot be demolished/catted below level 1.
As for your academy, when it is destroyed you will not lose any existing nobles, but you will not be able to educate nobles/mint coins in that village until you rebuild your academy.
Here are a few other pointers for what happens when various buildings are catapulted:
Resources: If your resources are catapulted to 0 (yes, this is possible), then they will continue to produce but will do so very slowly.
HQ: When catapulted, the build time for any upgrades currently queued will increase according the the new time factor of the HQ's new level. The HQ cannot be reduced below level 1
Barracks/Stable/Workshop: Any troops still in production when these buildings are catted or destroyed altogether will continue to be trained but at a much slower rate.
Smithy: You will not be able to produce any units that require a certain smithy level if the smithy is reduced to a level below that required e.g. you can't train Heavy Cavalry if your smithy is demolished below level 15 even if you have already researched them in that village. You will not have to re-research the unit once you have rebuilt your smithy.
Warehouse: The capacity of the warehouse will simply be reduced when it is demolished. If a warehouse is demolished and there are currently more resources in the village than can be accommodated, then the extra resources will be lost. The warehouse cannot be demolished below level 1.
Rally Point: When your rally point is demolished, you will not be able to send attacks or support, or cancel commands that you have sent. You will still be able to receive support from other players and they will still be able to recall any support they have sent to you. They will also still be able to recall any support they may have in your village. Any troops you currently have in transit will still be able to return home.
As for the market, I'm not too sure what will happen to your merchants if it is demolished. If they are all simply sat in your village, then I assume they will simply disappear, but I'm not totally sure what will happen if some/all of them are either transporting resources or if you currently have offers in the market.
I think that is all correct, please point out any mistakes I made. I just reeled that all off the top of my head :icon_wink:
