First of all I have never stated that I believe that the earth is 6,000 years old. I belive that the majority of fossil bearing strata from the Cambrian and up was laid down in a global flood 6 to 12 thousand years ago.
- Cave paintings and human remains and artifacts that are much older than 6,000 years
Since actual historical records only go back about 5,000 years these cave paintings, human remains and artifacts cannot be proven historically to be "35,000 or whatever years old". Many of these dates are generated from a comparison of C14 in them to modern amounts of C14. However, since according to the creation/flood model there was less C14 in the atmosphere in the relatively recent past such dating does not invalidate a recent creation.
- Ice core drills that show what chemicals were in the atmosphere over 6,000 years ago
These Ice core drills are based on evolutionary assumptions. Ice core data can also be interpreted according to various creation models.
- The fact that we can see stars being born and dying many thousands of millions of light years away, which means the universe is billions of years old, or at least much older than 6,000 years
The we can see stars being born and dying many thousands of millions of light years away does not necessarily prove that our earth is older than the creation model states. There are also creationist theories as to star-light and time, these are of course speculative, just as evolutionary cosmologies are.
- Rocks have been measured with independent isotope dating methods and have been shown to be much older than 6,000 years
Yes and many of these independent isotope dating methods give widely discordant ages even for the same rock. Also newly formed rocks which should give a hypothetical zero age, do by isotope dating methods give "ages" in the "millions" and even "billions" of years.
- The abundance of fossils that show that there has been way too much life on earth to be supported in the short time span of 6,000 years
These "too many fossils" calculations are often based on calculations generated from fossil graveyards, and are hense very innacurate. Also the creation model proposes different living conditions before the flood which would have supported a great deal more life than what we see today.
- Too many species of animals to have evolved from 200 or so kinds since the alleged Noah's flood 4,000 years ago
Who believes that todays species evolved from ONLY 200 or so kinds since Noah's flood? Most figures that I've seen show about 6,000 kinds on the ark.