> "Why do monkeys still exist, if humans evolved from monkeys?"
We didn't. Our last common ancestor with the monkeys existed a long time ago: about 27 million years ago.
At around that time, the primate order branched into different populations - some of which would evolve to become modern monkeys, and others which would evolve to become modern apes.
The ape family similary evolved and diverged, eventually giving-rise to the first Great Apes about 18 million years ago.
About 12 MYA, some of these apes migrated east out of Africa, nd they would eventually evolve into Orangoutans; 8 MYA, another sub-population migrated to highland "montaign" rainforest and began evolving towards being gorillas about 8 MYA; 4 MYA, the some of the remainder migrated out onto the savannah, where they began evolving towards being humans, and the rest stayed in the lowland jungles and evolved into chimpanzees.
> "Did God create both human and monkey separately?"
No. Modern monkeys all evolved from the primates which did not become apes 18 MYA.
> "Is Evolution still a 'work-in-progress' and we don't really know?"
Evolution is perpetually a "work in progress" - but these things we have a pretty good idea of.
> "If something evolves, does the original which it evolves from die out?"
If there has been no branching; no splitting of the original population into two or more sub-populations, then yes. The original population must all evolve in the same direction.
If there has been splitting, however, then one sub-popultionm *may* evolve faster and diverge more rapidly from the ancestral population than the other. So one of the new species would be more different from their ancestors than the other.
> "Or I could ask: why are there no Neanderthal men still in existence but there are monkeys?"
Neanderthals were a single species of Great Ape; there are 264 known species of monkey still alive now. I'm sure many more have gone extinct.
Furthermore, Neanderthals competed with Homo sapiens for resources, as we were very similar. It seems that we were the species "more fit" for the environment, so we out-competed them.