I would also like to see you -- or one of the other detractors -- address the scientific reasons. God created the universe. Why did he create it with the appearance of great age if it is less than 10,000 years old. That's not just a science issue but a spiritual issue as well.
YOM, is not a biblical reason. Yom can mean something like "Days of yore" but it can also mean "1 day" so in context with numbers (first,second, third) and coupled with "mornings" and "evenings" would biblically suggest just that a Day..(it actually has very similar usage to Day of English)
You admit that yom can mean something like "days of yore." Isaiah 30:8 says, "Now go, write it before them in a table, and note it in a book, that it may be for the time (yom) to come for ever and ever." This is just one example of the many times that yom is use to mean an indefinite period of time -- in this case, eternity.
The word yom has multiple meanings. Use the meaning of the word that most fits with what God has shown us from his creation, It's much easier than trying to force creation to fit to a single narrow meaning of a word.
Adam introduced sin...was Adam real?
Yes, Adam and Eve were real persons.
you still have the problem of death before sin
I believe that the physical death of plants and animals existed in the world before Adam and Eve. Lions and tigers were designed to be carnivorous. Bats were designed to catch and eat flying insects. Some bacteria eat other bacteria. The Venus fly trap and the pitcher plant are examples of plants that eat insects. And why would snakes be designed with fangs and poison if it were not to be used against other animals?
Why was there the physical death of plants and animals before Adam and Eve? I don't know. One thing to note is that "the LORD God planted a garden eastward in Eden; and there he put the man whom he had formed. the LORD God planted a garden eastward in Eden; and there he put the man whom he had formed." (Genesis 2:7). God expelled Adam and Eve from the garden after the fall -- to me, that says that the Garden of Eden was a special place on the earth unlike any other place. Some have theorized that Adam and Eve were created to redeem creation from the ravages of Satan. I don't know, but it's possible.