I don't have a weekly or monthly prompt, and tend to favor quality over quantity when it comes to prompts, but after a few years, they have tended to add up.
Some are whimsical and mostly free writing. Some are extremely structured and will require you to write exactly the amount or time that they call for. While each "rule" in a prompt often has a reason (most people write better under a time pressure than they do with none, for example) the only real rule with any prompt is to get you writing, so if you feel inspired by parts of the prompt but not the rest, feel free to cheerfully ignore whatever isn't quite working for you.
It's All About the Food Recombine, Reconfigure, Reconstruct
Sunday Prompts--Disney Style Fast and Random
Get Into The Head of Your Characters Metaprompts: The Prompts About Prompts
Concrete Detail Dental Writing Prompts? Oh yeah.
Writing as a Child Truth and Compassion...And Politics
Make Yourself Aware of Filtering Significant Details Eulogy
First Sentences Practice Daily Goal Setting
Sonder: Deepening Minor Characters The Paradox of the Human Condition-A Civil War Prompt
From a Slightly Different Angle NaNoWriMo Warm Up (best done before NaNo)
A New Year's Inventory What Does Success Look Like?
Look Down Your Own Mountain The Genre Shell Game
Pinterest Story "Scene 2"
What Have You Done for me Lately?