The biblical texts do not specifically address fixity of species except with the words "according to their kind." Science has a hard time defining what constitutes a "species" let alone a "kind." I figure there will be some latitude amidst kinds, much as the human race as observed today contains everything from dwarfs to giants; white to black, and much in between. The biblical texts would not propose any kind of "magical barriers." God is the source of everything natural, just the way it is.
For example, that we share a common ancestor with apes goes against YEC.
Not really. A Common Creator will quite obviously produce a result that could be construed as common descent. As for the history involved, yes, I disagree. And that is because no record of history denotes a gradual progression from ape forms to human forms. The best evidence is always in fossils and bones for some reason, but never in written records by those who themselves conduct science, namely humans.
The earth is 4.5 billion years old.
While that assertion resides within the hearts of many, it has not been empirically proven. Take some time to study the nature and concept of time, and put it together with quantum mechanics. What we are faced with in this life is too tentative to make an assertion such as yours as if it were a hard boiled fact.
At bottom, I fit the definition of theistic evolutionist, but if you care to strip me of that title I will not be ashamed in the least.