What Strange Behaviors Occur with Module Scripts?

1) This is an extreme case, and I wouldn't rely on its behavior. I doubt that this could happen if you aren't purposefully trying to recreate this.

2) I'm not sure what you mean by that. The point of a ModuleScript is that identical code can be used in more than one place. If you want variables specific to a script, define the variable inside the script, not the ModuleScript.

3) Please clarify. Do you mean different scripts requiring the same module, then calling a method of that module at the same time? In that case, they would run simultaneously.

If I am grievously wrong, please correct me. I wouldn't describe myself as a beginning scripter but my knowledge of ModuleScripts could use some dusting off.

lets say you have 3 module scripts module A,module B, and module C.

if module A requires module C, and Module B also requires module C and A. The code wouldn't run at all.. There won't be errors or anything. When I first encountered this situation, I literally debugged the code for 6 whole hours. reading the code over and over and over again, and adding a bunch of print statements everywhere.. basically if a module requires another module which requires another module that the previous module requires, then it causes weird behavior

No variables are not global if declared in module scripts.a module script can return a value which can be accessed by whatever script that required.. if the returned value is function, then that function can access all the variables in the module. doesn't matter where its called from.

Yes, a function can run multiple times. the following is valid;

In a module script:

local module = {};
local count = 0;
function module.countdown()
    for i = 10, 0, -1 do
        count = count + 1
        print("call #"..count, i)
    end
end

in a script:

local module = require("the module above")
while wait() do
    coroutine.wrap(module.countdown)();
end