A headset, if you don't have one, stem, spacers, and handlebars will round out the frame. If you want a road bike/tri bike, get a set of drop handlebars and some clip-on aerobars. If you want a true tri-bike, get a set of cowhorn bars and good aerobars that match up with them. Next, you need what we call a kit: the brakes, cranks, derailleurs, shifters, brake levers, bottom bracket, chain, cassette, and wheels. If you get a traditional road bike, the shifters and brake levers will be one piece, referred to as a brake/shift lever. If you build a tri-bike with cowhorn bars, you will need bar-end shifters on the aerobars and aero brake levers for the cowhorns. Kits can be made by Campagnolo, Shimano, and SRAM. Each is a bit different and has different levels of components, but no one maker is really better than the other...its all preference. Finish the bike off with the cables, and you should be set. Talk with your local bike shop to buy parts and get the sizing right.
As for the second question, yet, you can, but it would be a bit of a waste for a tri-bike. If you want to, you can get flat-bar road shifters from both Shimano and Campagnolo that match up with their road kits.
