Also there were a bunch of chimps beating up another one (because he had an undesirable personality) and when they stopped the victim climbed up a tree and another chimp (with a higher status) got near him to stop the other chimps from beating him up again.
Very few animals are capable of actions like this. The current belief is that most great apes and other mammals do have the ability to empathize with others, in the sense that they feel stressed when they notice others are in trouble, but aren't able to translate those feelings into actions. Chimps are the smartest of the bunch and have shown themselves to be highly social, but they're really the only ones, and their abilities are still miniscule compared to even the earliest humans.
So they do everything we do but in a smaller scale (because they don't have the same motor coordination we do).
Hardly. There are still fundamental differences between chimps and humans.
If you're interested, try googling for the PCDH11X and PCDH11Y genes. Chimps are said to have only one, on the x-chromosome, while humans have two. This is possibly the reason why we developed so differently from our common ancestor. Unfortunately when I look for it on Google I find mostly research information and not many easily readable articles.