I do not know, let alone understand the techniques used to age rocks. So I cannot comment. I have however, no problem with rock being of that age, or that there no human or mamal fossils in that age.

On the subject of carbon dating I do know a little
My understanding is this (in simplistic terms)

1) There are two forms of carbon in the environment in a known ratio
2) One of those forms of carbon is radio active and decays back to the non-radio active form, at a known and constant rate.
3) Living organisms also have these two forms of carbon in the same ratio up untill the point they died.
4) By measuring the ratio of these two carbons of a dead organism, we can calculate how long ago they died.
5) As measuring tecniques improve so does the accuracy of the calculation.

Cool, and this has been definitely proven to work .... I agree, yes it has.

My concern with it is the assumption that the ratio has always been the same as it is today. If, the ratio 10,000 years ago was half of what it is today then things that died 10,000 years ago would appear to have died 20,000 years ago.
Conversely it the ratio was double then it would appear to have died only 5,000 years ago.

Since the ratio between the two carbons is dependent on the amount of ultraviolet light entering the atmosphere this is a very real problem, it is one of the things scientists are trying to determine by drilling ice cores, has the ratio changed over time? Indeed, has the ratio oscillated over time? That would be worse because it would mean that it would become impossible to carbon date anything because you would have to know exactly when it died in order to know which starting point to apply.

Thats the problem with science, it can only interpret the facts based on current knowledge and if there is anything that evolves it is definitely "current knowledge".
So, unless you believe as one scientist I have heard, "Science is dead, we now know everything", then there is no firm ground for you stand on while you make your absolute assertions that your beliefs are based on "solid evidence"