In this chapter, Moses gives us laws on various topics and then a series of laws governing sexual morality.
This chapter begins with a list of largely unrelated laws, which I will address in order.
Verses 1-4: This passage is largely similar to Ex 23:4, except that it now speaks of helping your "brother" (usually rendered "countryman") instead of helping your "enemy". It also expands the scope so that you must help them with anything that you find lost, like garments or other possessions.
Verse 5: This command is similar to the prohibition of homosexuality, because in both cases the main emphasis is on adherence to gender roles. With homosexuality, it is a prohibition of having sex with a man the way that you have sex with a woman (paraphrase, Lev 18:22). In this case, it is a prohibition against a man dressing as a woman, or a woman dressing as a man. In that sense, we can look at this passage as an implicit confirmation that the bible also prohibits lesbianism, because that is the proper generalization of gender roles as the bible understands them. I discussed homosexuality in depth here. Interestingly, in that discussion I state that Lev 18:22 doesn't prohibit lesbianism, which is technically correct, but I think v. 5 of this chapter shows that a black-and-white analysis might not be correct. We have to deduce 1) the author's original intent and 2) how to translate that intent into the modern societal context.
That's why I cringe whenever I hear various sources suggest that on the basis on v. 5, women should not wear pants, because in our society women wearing pants is generally an acceptable form of "women's clothing". I do think that certain ways of dressing are inappropriate, but it always depends on the context and the intent. Namely, dressing for the purpose of confusing gender roles is probably inappropriate. Again, there are exceptions, but that is how I would interpret this law.
Verses 6-7: This reminds me of the "not boil a young goat in its mother's milk" law (Ex 23:19), because the core issue is respect for animals. This law does not prohibit the Israelites from taking the young, just as Ex 23:19 doesn't prohibit them from boiling the young goat it simply asks that they show respect for the animals by not taking the mother with the young (or boiling the young goat in its own mother's milk).
Verse 8: And thus, tort law was born. You are responsible for accidents that occur due to your own negligence. If Moses could have seen what tort law would become in our country and in our day, maybe he never would have written this verse. Oh well, what is done is done, for better or for worse.
Verses 9-11: These commands are largely equivalent to Lev 19:19. As I briefly addressed in discussing Lev 19, I think these laws are meant as an extension of the principle of separation (I have written about this principle many times before).
Verse 12: This is basically copied from Num 15:38-39. The tassels are also conceptually similar to the tefillin and mezuzah that remind the Israelites to always remember the commandments of the LORD.
After that is a section discussing sexual morality, which is a series of laws relating to the 7th commandment, you shall not commit adultery. It begins with a procedure for handling when a husband "charges [his wife] with shameful deeds", that she was not a virgin when he married her. I've discussed Hebrew marriage practices with reference to Dinah's rape, and this chapter gives us some additional context for understanding that. It also gives us some context for when Tamar was nearly put to death for committing prostitution (Gen 38).
It seems deeply ironic to me that Tamar could be put to death for prostitution, while Judah faces no punishment for doing the exact same thing. We see the same imbalance here, where a woman can be killed for having sex before marriage, while the man only faces a monetary fine if he lies about his wife. This surprises me because we know in other places that the punishment of false testimony is "you shall do to him just as he had intended to do to his brother" (Deut 19:19). From that, I would have thought the punishment to the husband for his false testimony would be death. I don't know how to explain the discrepancy.
In general, men in the OT do not face any punishment whatsoever for having sex before marriage. This imbalance is inherent to the culture of polygamy, because men are allowed to have multiple wives but women cannot have multiple husbands. Men can still be put to death for having sex with a married woman (i.e. adultery), but not with an unmarried woman. In that case, the woman more or less becomes an additional wife for that man, as we see in the second half of the sexual laws.
After the "virginity test" is a series of four situational laws that cover different cases that may arise. It first states a general principle, that a man having sex with a married woman results in the death of both of them. However, there are two conditions that determine how they should be treated.
First, if the adultery happens in a city versus a field. If it occurs in a field, the presumption is that the attacked woman cried out but nobody was around to hear her cries, and therefore only the man is guilty. If it occurs in a town, then the presumption is that the woman did not cry out, because people were around but nobody was alerted to stop the crime. Therefore the woman must have been complicit and therefore must die.
Second, if the woman is married, engaged or unmarried. If the woman is married or engaged, then she must not have sex with another man for any reason. If the woman is unmarried and not engaged, then a man who has sex with her (whether in the field or in the city) must pay a bridal price and marry her for life. To many people, it seems a cruel fate for a woman to be forced to marry her rapist (if he attacked her in an open field). At this point, I should remind my readers that if a woman is not a virgin, she might not be able to find another husband. Certainly it becomes harder. While the bible isn't entirely clear what happened to Tamar, she is never described as being married after what happened between her and Shechem. In fact, she is barely mentioned at all, suggesting that while she lived, her life never really recovered.
Being assigned to a husband guarantees her a right to food, clothing and shelter, as well as the possibility of raising children through her husband. So we should understand that this law is both punitive to the man but also protective of the woman, however awful it may look to modern eyes. This is why the man is forbidden to divorce the woman, because he is now required to materially support her.