You have mutual top-level imports, which is almost always a bad idea.

If you really must have mutual imports in Python, the way to do it is to import them within a function:

# In b.py:
def cause_a_to_do_something():
    import a
    a.do_something()

Now a.py can safely do import b without causing problems.

(At first glance it might appear that cause_a_to_do_something() would be hugely inefficient because it does an import every time you call it, but in fact the import work only gets done the first time. The second and subsequent times you import a module, it's a quick operation.)

The issue with the error "module has no attribute 'addition'" likely arises because Python may be trying to import the script incorrectly due to naming conflicts or caching issues in Jupyter notebooks. Here are the steps to resolve this:

Rename the test.py file to something other than test (e.g., my_test.py). This avoids conflicts with Python's internal test module.
Restart the Jupyter kernel after renaming and re-run the notebook.

You can't add properties to bge.logic.

To get this to work in the game engine, add a game property to the object and adjust your script to get the controller to access the property.

import bge

cont = bge.logic.getCurrentController()

input = []
for i in range(2):
    input.append([])
    for ii in range(cont['DnpolymeraseNum']):
        if i == 1:
            input[i].append([0,0,0,0,0,0])
        if i == 0:
            input[i].append([0,0,0,0,0,0,0,0])`

The problem is submodules are not automatically imported. You have to explicitly import the api module:

import myproject.mymodule.api
print myproject.mymodule.api.MyClass

If you really insist on api being available when importing myproject.mymodule you can put this in myproject/mymodule/__init__.py:

import myproject.mymodule.api

Then this will work as expected:

from myproject import mymodule

print mymodule.api.MyClass 

This may not be the cause for everyone, but I've identified at least one set of triggers.

1. Run Python toolbox tool from ArcCatalog
2. Geoprocessing history is on and includes a result from #1.
3. When starting a new ArcCatalog session, no geoprocessing windows are open initially (such as ArcToolbox window, Python window, Results window).

If the above are all true, the Python toolbox tool will show the AttributeError: 'module' object has no attribute 'Parameter' exception.

Clearing out the history (or not logging it at all) will avoid the issue, probably why I didn't see this before as I rarely retain my history.

Right-clicking on the toolbox and using refresh will clear the error, but it will come up again in the future as long as the list above remains true. However, if the tool is importing the tool class from a separate tool file (like the case above) a refresh will not be enough. For that, I had to force it by including a reload in the .pyt, and then a refresh on the toolbox will clear the error.

# Using example of toolbox.pyt above
import toolpackage.configurator  # add import
reload(toolpackage.configurator)  # add a forced reload
from toolpackage.configurator import ToolboxConfigurator