To save money? Absolutely not. I'm keeping a spreadsheet on our 20 chickens this year. They're young, so input is very high while output is still ramping but I'm guessing it's $7-8 dozen in food costs alone (the highest end organic feed tho), never mind the initial buyin.
What is the amount of time required for all the different chicken activities? (estimated weekly average)
Once you have it set up, I'd say no more than about 2 hours per week. The feeding and watering can be automated, so it's really just whatever cleaning or optional shuffling of their locations you do. Checking for eggs can be done in a few minutes, and you technically don't have to do it every single day. You might actually choose to spend more than the minimum to tame them and treat them as pets.