Save PDF in black and white with given DPI using Python

Question

I have a Python program doing some manipulation on PDF file names.

My colleague has asked if I can:

1. Open each PDF and save with the new file name, and
2. Change the PDF to black and white (remove any colour), and
3. Save with a fixed DPI of 300.

I'm vaguely aware of reportlab and pdfrw but don't know if they, or other libraries, can do these operations.

Any example code would be much appreciated.