Refreezing stock after boiling

Can I safely refreeze stock that I have brought to the boiling point?

If so, should I boil it or bring it above a certain temperature for a certain length of time to ensure food safety?

Is the presence of fats or oils a point of concern for rancidity or food safety?

Finally, are there some kinds of stock (vegetable/fish/meat/poultry) that need to be handled differently? Or will boiling suffice for any liquid preparation (soups, reductions, gastrique)?