Does storing ground coffee in a freezer make it stay fresh longer? If so, how long will it remain fresh?
No. In fact it's likely to make your coffee taste bad, and gum up your grinder. You should store your coffee in an air-tight container, at or just below room temp (about 25 degrees Celsius).
Coffee can and will absorb all kinds of odors, and while your freezer probably doesn't smell like much, there are odors that will (at the minimum) dull the taste of the coffee. Additionally, when you take your coffee out to room temp, condensation kicks in which further degrades the beans and messes up your grind. Depending on your climate, the condensation can also invite mold. Yuck!
The only time you should be freezing or refrigerating coffee is when you're doing so because you've created a desert with some :) Otherwise, dark air-tight containers are the best way to go, just store them in your cabinet.
A good rule of thumb: Store anything you buy the way it was when you bought it, unless the label tells you to do something different once you open it.
Freezing coffee is fantastic, but only if you do it correctly, and if it's not going to be consumed within the first 2-3 months after the roast date. It's surprising how much fragrance and flavor is kept when done correctly even after sever months past roast. If you freeze coffee, make sure it's as air tight as possible. Ideally you would want to vacuum seal individual packets of coffee, so that the rest of the coffee isn't disturbed once opened. After the coffee has defrosted in the slightest though, it can not be refrozen.
Here is in interesting article from Home-Barista about doing blind tasting of frozen coffee versus fresh: Coffee: To Freeze or Not to Freeze