Hi! Have you heard of Lang-8? it's a website more tailored towards what you're looking for, If you can't find a language partner here i suggest trying it. Good luck! 

yes you've learned should correctly, the use in these examples sounds like very proper and outdated speech. It's something Sherlock Holmes would say. The first can be thought of like this: It's strange that he would think it's good to be here, He's usually on time This is a strange example because implies the speaker is somewhere he doesn't expect the subject, him, to be. for example: He wen't to the man's house to investigate, expecting the man to be at work, looked in the window to check the house is empty and was surprised to find the man to be there! he thought to himself "It's strange that he should be here. He's usually on time". for the second example it's a little like: "I was surprised that he would think it's good to say such a thing" this example is a little more self explanatory. I hope this wasn't too confusing, please feel free to ask about any of this that doesn't make sense.

as a native speaker i can't see much difference in everyday conversational speech, I guess the three versions feel a little different. but you don't need to worry about it unless you want to study literature. The one that stands out the most to me is the third one, it sort of implies she asked ONLY you for help and nobody else. I think there are three because Help can be treated as a verb (something you do like in the first one "to help") and it can be treated as an object (something you give like in the second two "for help, my help"). So don't worry about which you use, all 3 are good in any situation.

wake is a verb, it's something you do for example to wake up from sleeping awake is something you be. for example question: are you sleeping? answer: no! I'm awake a way to remember this could be: if you wake up, you are awake.