What are the pros and cons of importing a Python module and/or function inside of a function, with respect to efficiency of speed and of memory?
Does it re-import every time the function is run, or perhaps just once at the beginning whether or not the function is run?
Does it re-import every time the function is run?
No; or rather, Python modules are essentially cached every time they are imported, so importing a second (or third, or fourth...) time doesn't actually force them to go through the whole import process again. 1
Does it import once at the beginning whether or not the function is run?
No, it is only imported if and when the function is executed. 2, 3
As for the benefits: it depends, I guess. If you may only run a function very rarely and don't need the module imported anywhere else, it may be beneficial to only import it in that function. Or if there is a name clash or other reason you don't want the module or symbols from the module available everywhere, you may only want to import it in a specific function. (Of course, there's always from my_module import my_function as f
for those cases.)
In general practice, it's probably not that beneficial. In fact, most Python style guides encourage programmers to place all imports at the beginning of the module file.