Yes, yes, and yes. The "staling effect" in coffee is very well understood, but unfortunately that hasn't yet been recognized in the marketing and sale of most coffee in the United States. For a great overview of the mechanisms and their effects on taste, have a look at this overview of coffee staling
The short answer to how coffee stales is simple: tincture of time, multiplied by exposed surface area (whole bean versus ground), and made worse by exposure to heat, air, water, and sunlight. And the most obvious outcome is immediately perceptible in coffee taste, as bitterness (it's literally rancid).
What's amazing is that despite a massive cultural shift towards every shorter food supply chains, with an emphasis on local production and freshness, people still treat coffee as a durable commodity, as opposed to a perishable one, which it is.
Our rule of thumb is pretty simple: coffee is at peak freshness between two and fourteen days post roast. When you buy coffee, buy whole bean only, and grind just before you brew. Most importantly, when you buy, insist on a "roasted on
" date as opposed to an expiration date.