I would say that reading them often and pointing them out will help you learn them better. You can also find phrasal verb books filled with examples and explanations; you can find these online and possibly in local book stores.

This sentence is okay. If it sounds strange to you, you could say "I had to drop out of high school, so that I could take care of my family."

They have the same meaning, specifically in terms of geological features. They just have different origins as words. I believe 'Dale' is used more often in the UK, whereas 'Valley' is used more in North America.

I think that in this context, it is saying that people weren't as connected, people and news traveled slow, and it was as if they lived in unconnected worlds.

Usually within context, it is an idiom that basically means 'flirting'. So if I am "hitting on" someone, I am flirting with them.

"Tenth Street Washington house of William Peterson, a tailor" This is using an older form of English. It means that in Washington (D.C.), on Tenth Street, the house of William Peterson who was a tailor. Think of it as "William Peterson, who has a house on Tenth Street in Washington"

I can't think of any specific kind of "area" for things that need to be repaired. It really depends on what it is that needs to be repaired and then the answer for that can be different. For example, if I have an appliance that breaks, I take it to an appliance-repair shop. If something is broken on my car, I take it to an auto-repair shop. Let me know if you have any more questions. :)

There is no difference in the meaning. They are synonyms... two words that share the same meaning. In English literature, 'slay' is often used more in terms of combat, even though it has the same meaning as 'kill'.