Genesis 1 is a basic chronology of the Act of Creation. Genesis 2 is clearly a retelling of individual days. Genesis 2 does not indicate that the animals were formed after man; it's simply a secondary mention of the fact that they were made, then brought to Adam after he was made. Obviously, they were brought to him on the sixth day . . . the same day that Eve was formed.
As far as Adam's age, he did "die" on the day that he ate the fruit in the sense that he instantly transformed from an immortal to a mortal--his mortality signifying that death now presided in his body. His immortality "died" that day. To "die" in Hebrew does not necessarily mean to fall down dead at that instant (though it can; it depends upon context). It can also mean to fail, to perish, to (be) destroyed. His perfection failed and was destroyed in that day. He perished from perfection into sin; from eternal life into physical death.
Here's another thought: John 3:16 says that whosoever believes in Jesus will not perish (die) but have everlasting LIFE. Does that mean that when I'm old and feeble, I'll never see a grave? Clearly not. The wages of sin are death; we are all sinners; we all die.
What about these passages? "Jesus said unto her, I am the resurrection, and the life: he that believeth in me, though he were dead, yet shall he live: And whosoever liveth and believeth in me shall never die. Believest thou this?" (John 11:25-26)
Does this mean I'm immortal? Not in my physical flesh per se; but Jesus Christ grants me eternal LIFE through Him rather than to perish and DIE by spending eternity in hell. DEATH and hell are cast into the Lake of Fire ultimately. Those that are judged at the Great White Throne Judgment (which, quite frankly, have just been raised from the DEAD, brought back to life, and then have DEATH pronounced upon them again . . . huh?) and found ungodly will be cast into the Lake of Fire. This is the Second Death. We are limiting the definition of "death" by our mortal understanding, but "death" is far more involving when we transcend our earthly plane and involve eternity and a host of extenuating spiritual applications. Adam and Eve did not know death before eating of the Tree. They knew death the instant after, as it overtook and canceled out their immortality.