With regard to buying the component group you linked to:

"What do I need to make it play nicely with Campagnolo parts?"
If you are going to buy the Campy group like you mentioned then that will come with everything you need to make this "play nicely" with Campagnolo parts except your rear hub. To make this work you would need to find a cassette that uses shimano/sram splines but has campagnolo spacing or you will need to change the freehub body if possible to a campy compatible one.

"If I bought the centaur groupset here, would I need to buy a new ultra-torque bottom bracket or would it come all ready to fit?"
The product discription on the webpage you link to mentions that this component group comes with the bottom bracket cups. The bottom bracket spindle is integrated into the crank arms already...so no you would not need to buy a separate new ultra-torque bottom bracket.


"Would the cassette fit on my Formula hubs, or would I need to buy new wheels to accommodate it?"
Your front hub will not be a problem but if your formula hubs are from your current bike then the rear hub is shimano/sram compatible...it would not be compatible with campagnolo cassettes unless you are able to change the freehub body to one that is campy compatible.

"Would the caliper brakes that come with the Centaur work with my bike, which came with cantilevers? If not, would my cantilevers work with the group set?"
If your fork and rear stay bridge are drilled to accept a caliper brake then it could work...you should check with the manufacturer to get a definitive answer if the fork and seat stay bridge are designed (read strong enough) to mount and use a caliper brake on your bike. If you stay with your current cantilever brakes you should be able to use the campy ergo levers with them...I can't comment on how they might perform but perhaps someone else will be able to chime in with that info.

I am a campy fan myself but have ridden many miles on shimano stuff as well. Without trying to start a war about which is better campy or shimano, I have to ask why you think you are upgrading from what you have by purchasing and installing the campy group you have linked to? Or a better question is...what do you hope to gain from doing this "upgrade"/what benefits do you perceive you will attain? I am not one to get in the way of anyone who wants to spend their hard earned cash but I am just wondering if there is something wrong with your current components that require a change.

-j