TRI BIKE

1. The best thing you can do is get a fit BEFORE you make a bike purchase - that way you know you are paying for a bike that will fit you properly.  It's likely the fitter will suggest a bike(s) you've not even considered.  It will be the best $$ you spend.  You can find a reputable fitter in your area here.
2. NO!!! You do NOT need to pay the ridiculous amount of money the manufacturers would like you to believe you need to spend.  Recently a wind tunnel test was done that arguably proved the mid-level triathlon bikes are only a couple of watts slower than the ultra high-end superbikes.  The simple reality is you can put Sebastian Kienle on a Walmart road bike and he will consistently beat every age-group athlete in virtually any triathlon.  It isn't about the bike - it's about the engine.  There is no rule that says you MUST ride a "triathlon bike."  If you find yourself at some point competing at the very highest level you may wish to consider a high-end bike.  You DON'T need that to get started.
3. The list is endless where you can locate used bikes - Craigslist, BT Classifieds, Slowtwitch Classifieds, E-Bay to name a few.
4. See #2 above.  There is no reason you can't do any triathlon of any distance on a road bike.  If you ultimately want to challenge for an overall podium finish, qualify for Kona, etc., you may want to consider a quality "triathlon bike."  Certainly at most sprint and Olympic distance events you will see "Beach Cruisers", Fat-Bikes, Mountain bikes, Hybrid bikes, Road bikes, and yes triathlon bikes in transition. As you go up in distance the ratio begins to favor triathlon bikes, however it won't be uncommon to see road bikes at even 140.6 events.  At the end of the day, it's about the engine.  Additionally, if you can't maintain aero for the distance of the race, being on a triathlon bike is a waste of money because you will be slower sitting upright on a triathlon bike than you would be on a road bike.

Hope that helps.

There are a few online fit calculators.  They're not a replacement for a proper fit, but can be used to start your search.  

Tri bikes are expensive.  Capitalism at it's best!  Volumes for tri-bikes are significantly lower than road bikes so design cost has to be amortized over a smaller volume.  

Yes, you can shop BT classified ads, craigslist, cycling forums.  I got my tri bike from Ebay 12 years ago.  

Ride a bike that fits and that is comfortable.  Maybe it's a tri bike, maybe it's a road bike with clip-ons, maybe it's a straight up road bike.  My experience is that clip-ons/aero gets 1-1.5 mph.  If that's 17 mph to 18 mph, you'll cover the 56 miles 11 minutes faster on the tri bike.  Are those 11 minutes worth $500 more on the bike?  I too have seen mountain bikes on HIM courses.  I've also been passed on my tri-bike by a mountain biker as if I were standing still.  Ride lots and ride smart and you'll do well whether it's a roadie or tri bike.