Is it obligatory for me to fast the entire month of Ramadan after childbirth, breastfeeding, and childcare in Western countries, or is it permissible for me to pay a monetary fidyah for it?

You must make up for the fasting when you are able to do so, on days when you are free from any impediments. The religiously prescribed fast extends from the break of dawn until sunset. The long duration of the fast is not an excuse to waive the make-up fast. You may delay making it up until you are able to do so. The obligation to make up for the fast does not shift to feeding the poor except for a chronically ill person whose recovery is not expected, or for an elderly person who is unable to fast.