Slavery: Yes and no. While slavery was a part of the Bible times, it has a different connotation of what we're more familiar with today, or in the sense of Egyptian slavery of Israel. Slavery was more of a servanthood status. It was a way to pay off debts, and people often learned trades. There was also a term limit for slaves (7 years), as evidenced in Genesis, when Jacob served his uncle for 2 slave terms for his wives (yeah, yeah, polygamy was in the Bible, too, even though one book over enforces monogamy). Buying and selling people into slavery, however, is frowned upon.
Death penalty for Blasphemy: With the book of Leviticus, there definitely seem to be some gray areas (from what I gather) as far as A LOT of these rules as they apply to the New Testament era. I'm guessing you're referring to Leviticus 24 (that's how I Google searched it). With the Pentateuch era, there was no Savior, and Adam and Eve completely blew it when they sinned against God, so pretty extreme things had to be done to be kept pure, and yes, this was limited to a small part of the population. Why? I don't know. I'm not theological scholar. As far as blaspheming nowadays, that wouldn't get you the death penalty physically. Ultimately, however, you're blaspheming against Almighty God. Thankfully, Jesus' death and resurrection made Him the Intercessor and Saviour for all our sins. God never calls us (New Testament era) to kill people on His behalf.
Death penalty for idolatry: Kinda like the blasphemy issue. Again, because of the pre-Savior times, the Israelites were called to do things by God that not even they could get away with today.
R@pe victims: Yeah, not like women had much in the way of modern rights back in the Old Testament / Pentateuch era. But even with that, it's meant to make the man who defiled an unbetrothed virgin woman (have sex with her consensually or by r@pe) to take responsibility for defiling her. (Deuteronomy 22:28-29) Not only would he have to marry her, but he couldn't divorce her, and back then, men could divorce for ANY reason. Now, here's the kicker: if the woman's father refused to give his daughter to her r@pist -- an understandable decision which I'm sure happened a lot -- he would force the man to pay a fine (Exodus 22:16-17). In that sense, justice would be served on the man, and the woman would not have to face her attacker again. Now, if the woman were betrothed/married, that's an instant death penalty for the man.
Sabbath: next comment.