Tuesday, Wednesday, and Saturday are cheapest days to fly, not necessarily to buy
Airlines carry fewer business passengers on these days of the week, and thus there's often a surplus of seats. But don't confused this fact with the idea that buying a ticket on a Tuesday will result in lower airfare. That's a separate thing.
You can cancel within 24 hours for no charge
Now, there are caveats, so don't go booking out an entire planeful of tickets just for S&Gs. For most airlines, you can cancel/change your ticket up to seven days before your scheduled date of travel and get a full refund. The notable exception: American Airlines, which instead allows you to hold a ticket up to 24 hours at the price you see. Additionally, you need to book directly with the airline's website, and not through a third-party booking site, although big ones like Expedia or Travelocity offer policies similar to those of airlines. But the big takeaway: you can have buyer's remorse for up to a full day. And some airlines -- like Southwest -- have even more generous refund policies that let you change plans up until right before you take off.