Look up the definition of fossil. It's fucking rare for them to exist (with it being impossible for a lot of species), and we're extremely lucky many of them do, of the ones that have actually been found. Heck, many of the fossils we've found could in fact be transitional fossils not representative of the average animal of their species.
And no, their populations needn't reach comparable levels. Often creatures evolved away from each other and some of them were LESS fit, but fit enough to survive. Those which evolved away also tended to evolve into niche areas, otherwise they would compete with that which they evolved from (often leading to one or the other going extinct). Also, when a creature evolves from another creature, that doesn't mean the older creature suddenly died - they often coexisted.
Further, Evolution at the smallest level is a discrete process. Small mutations in genes can cause profound changes which some people would believe require some intermediate mutation, but in fact don't.
What evidence do we have? Well you could always read the thread, otherwise, I'll link you to the American Botanical Society's statement on evolution, instead:
http://www.botany.org/outreach/evolution.php
Here's a bit of trivia for you: did you know all the house cats around today all come from one species 10,000 years ago when they self-domesticated themselves? In fact, they're still one species. Transitional organisms often still fall under their normal species moniker.
And one day people will have to admit that humans aren't one species anymore, as data shows our evolution away from each-other racially is accelerating. Still, while we can all reproduce without a certain % of failed births, we're for the most part one species.
And here's a question for YOU: If you don't believe in evolution, what DO you believe? That god created evolution, then every now and then changed an animal's DNA, only to wipe most of these experiments out later?