So you based your life's perspective on one book?
I've based my moral and religious guidelines upon the Qur'an, yes. Believe it or not, I was once an atheist like you, but I realized the errors of my ways and changed directions. I put in four years of due diligence on the Qur'an after countless years of exploring (raised Catholic, read numerous Buddhist texts), but I've never regretted my decision to become a Muslim. That was my best decision ever.
Do you follow EVERY teaching in that book, or do you just pick and choose the ones that fit your modern conception of the world?
I'm not a "cafeteria Muslim," no. I follow everything in the Qur'an that applies to me to the best of my abilities.
If you do follow all the "guidance" written in that book, you have a problem because many of the teachings are immoral and/or contradict one another.
Now you see, this is where your incredible ignorance of the Qur'an and Islam begins to show. It's very obvious you've read little, if any, of the Qur'an; not that I'm surprised.
I won't go into the numerous times that this book promises hellfire and torture for unbelievers like me...
Yeah? So? His universe, His rules, His rewards and punishments. What makes you worthy of heaven? Your good looks? The minimum requirements, according to the Qur'an, are a belief in Him, a belief in the Day of Judgment, and good works. All three, not just one or two of three. Ignoring the third, how do you qualify? How have you earned the right to go to heaven? This is either/or, not multiple choice. There's no special dispensation simply because you object.
...but it also says that those who believe in the trinity are cursed to hell.
Actually, the Qur'an says nothing of the sort; in fact, several verses (2:62, 5:69) say the exact opposite. Islam is not one of those religions that says only "we" are saved. There's no guarantee a Muslim will be saved either. You have to earn heaven, remember?
Do you agree that women are possessions of men and that men are "a step above" women?
Women as "possessions of men" is the Orientalist view, not the Islamic view. Men a step above women? No, not part of Islam either. The Qur'an does says in part: "Men are the protectors and maintainers of women, because Allah has given the one more (strength) than the other, and because they support them from their means..." (4:34). But that doesn't mean men are a step above. Men and women in Islam have equal responsibilities. If anything many Muslim men think that Muslim women have it easier than they do.
Do you agree that homosexuality is unnatural and to be condemned?
The underlying theme in the Qur'an is that life is most important. This is not explicitly stated in the text, but can be deduced from the Qur'an's positions regarding various issues regarding life, death and health. Thus, to preserve life and promote healthy lifestyles, sex is forbidden in all cases except between married couples. Thus, premarital sex is haram, adultery is haram, fornication between any non-married person, regardless of gender, is haram. Likewise, all anal sex, even between husband and wife, is haram as well. In Islam, two men or two women may love each other, but the relationship must be platonic. To take the opposite position is unIslamic and promotes unhealthy lifestyles. A lot of people don't like to hear that, but that's their problem and, once again, they'll have to answer for it on the Day of Judgment.
Why didn't Jesus or Mohammed condemn slavery?
I won't speak for Jesus (pbuh), but I will say that while the Qur'an did not expressly prohibit slavery, it did encourage slave owners not only to free their slaves if the latter asked for it, but to pitch in money to the slave so as to make it easier for them. If you knew the history of Muhammad (pbuh) and his companions, you would know that they freed many of the slaves in that time. Try reading the story about Bilal for a good example.
Which in my view renders the texts increasingly useless and invalid.
Your loss. Good luck on the Day of Judgment.