Yes.
Each world in minecraft is saved as a separate file.
If you open the start menu and search ".minecraft/saves" (without the " signs) you should be brought to a folder containing all your different world saves.
They will be named whatever you named them in the first place, eg.
JoeBlogs world.
Simply copy the world folder you want to the .minecraft/saves folder on the computer you want to play on.
Yes you can but you will not have have the worlds that you created on the other computers.
You can bring a flash drive in, and put .minecraft and minecraft.jar in the school computer and thus run the .jar and play minecraft offline, on any worlds.
delete your BIN and then run minecraft, it will then be cleared and restored, this doesn't change your worlds.
No it doesn't because it is just like force upating but you do need to update your worlds.
Copy the minecraft worlds from the file explorer
In a sense, yes, but in another sense, no. You do not need to install Minecraft to play it on a computer, you can simply run it in your internet browser on Minecraft.net. However, if you want to run Minecraft without an internet connection, or without visiting Minecraft.net, you must install Minecraft on your computer. You can install Minecraft on multiple computers under the same account, but your saved worlds will not sync between computers.
Nothing will happen if you keep installing and uninstalling Minecraft. Minecraft does not track how many times you have installed it nor does track how many computers you have it installed on. The only drawback is if you uninstall Minecraft by deleting the .minecraft folder you will lose all of your saved worlds on that computer.
you link it to your minecraft account
yes.
Minecraft
No.
No. The way LAN connections work is: Minecraft searches your network (what all computers in your home are connected to) for games to join. Through LAN connections you can't connect to anything outside of your network.