There are many more wise heads than me ... so I can only report on what many others have said.
"Fat Models, Helper Modules, Thin Views, Stupid Templates" i.e Put more logic into anything but views and templates;
In reply to your issues:
1. What has size to do with it? Split them up into different sub-files if you need to keep things short & then "import" them into the models file.
2. Custom managers are essentially fancy "filters" and not business logic - keep them short, focused and to-the-point.
3. Yes; if appropriate for your case i.e. you need logic shared across multiple places in your app/project (see also the stackexchange answer).
(4) Unit testing is a whole other story. But there is nothing particularly weird or obscure in this approach that could not be tested.
Finally, remember the Zen of Python:
If the implementation is hard to explain, it's a bad idea.
If the implementation is easy to explain, it may be a good idea.
HTH
Derek