Wow. 180?! I hope that's spread over two days. It can be done in one, but...I imagine things will hurt. A lot. When is this event?

No, SOs are usually not the best coaches. They want you to be successful, but they want you to be successful RIGHT NOW. (Ask me how I know!) Get thee a road bike, if you don't have one already. A decent one. If you're buying new, be prepared to spend a fair amount of money on it--you want at the very least Shimano 105 components for a ride that long. And you should also be prepared to spend a lot of time trying them out. The last thing you want is for your bike to become an obstacle. And get it fitted to you! Not just sized, fitted. They'll swap out stems, adjust saddles, etc so that you're comfortable.

Gears: Like everyone else has said, you change gears to keep yourself pedaling at a comfortable rate. What that means is different from person to person. Shift down (toward the frame of the bike) to make it easier (good for hills and when you're tired), up (away from the bike) to make it "harder" (this is good for going downhill and going really fast on the flats). How often depends on conditions--you, the terrain, wind...
If I figured it out, you can too. If you can, put the bike on a trainer (does the husband have one?), and play around, noticing how each gear feels. If you don't have a trainer, find a big empty parking lot and do the same thing.

How often: I ride 2-4 times a week, depending on my schedule. However, I've been riding for 3 years. I started out doing very short (around a mile) rides every couple days, then doing 1-mile laps around campus whenever time allowed (a couple times a week). You need to ride often enough to toughen up your butt, but you also need to find time to rest. That depends on you and your current level of fitness.

Clipless: I like my clipless pedals. I wouldn't ride long distances without them because they me spare my quads a bit and use my hamstrings. However, it took me nearly a year of irregular riding to feel comfortable with the idea. You shouldn't start with them right off the bat. Get used to the bike, and to cycling in general, then get yourself some clipless pedals.

Speed:
That depends on you and your group. I think in the neighborhood of 15mph is average for many groups, but there are slower and faster people out there. If it's a very large group, you'll get smaller groups separated out by speed.