If you wear it over a choli or tunic you wouldn't need to sew it to a bra, though of course you do need to deal with the chain/strap issue. If you want to keep it chain you could get extension chain at a craft store. Or you could replace the chain with ribbon/fabric straps. That would probably be more comfortable.
If you want to wear it without something underneath you should probably sew it to a bra. It will be more comfortable than bare metal and you won't show anything accidentally. Take the coin bra to the store and find a bra with cups that fit the coin cups. Dance bras are generally a bit bigger than underwear bras. You want the extra coverage when that's the only thing between you and the world.

Yes, that's what I've heard of people doing. If it's just put on ontop of a bra, it may shift around, making it look like you're just wearing your underwear underneath. What excess chain? Do you mean the chain that fastens in back? Does it not reach around to fasten in back? You could always head to a bead store and buy some matching cahin to fill in the gap in back. Otherwise, cutting it off would be an option. You'd just be breaking/openning the chain in one spot. It shouldn't damage anything else. And, if you want to put them back on, buy more jump rings to reattach them.

yeah.. I can google and bring up the troupe page, but I don't see instructions for anything, just the usual gallery, offers for lessons, etc.