No, Genghis, you're the one with the misunderstanding.
1 - Evolution doesn't require species X to die out when a new species branches out from it. Species only die out when something causes them to. Having one species split off from another doesn't necessarily mean the first can't survive any longer. Something in the environment has to change to kill off the original species.
http://www.pbs.org/wgbh/evolution/library/faq/cat05.html2 - Humans are primates. Every human ever born was born to primates.
3 - There is no 'missing link'. The missing link myth is perpetrated via ignorance, similar to the controversy over the 'gay gene'. If you get your science from the media or other non-scientific sources, you'll hear alllllllll about these 'controversial' topics. If you look at scientific literature, these terms and controversies don't even exist.
Every fossil is a transitional fossil. Each discovery simply increases the 'resolution' we have of the fossil record. We actually have a very good picture of the fossil record at this point, but you have to understand the fossil record is like a very large puzzle. We're constantly finding new pieces, and we've never found a piece that doesn't fit.
We have narrowed down the possibilities for the CHLCA(Chimpanzee-Human Last Common Ancestor) to a relatively small timeframe. Within that timeframe, there are several candidates, we just haven't found all the pieces yet.
Imagine a partially finished puzzle. You might not be done with it yet, but you can tell that over here is a tree, over here is a house, this is a lake, these are clouds. That's the point we're at with the fossil record. We haven't found every piece, but we have a very good overall picture.
4 - Again, the fossil record is only
one line of evidence for evolution. Check this out for a very basic overview:
http://www.evolution.berkeley.edu/evosite/lines/index.shtml
Edited 1/16/2015 05:37:48