1. I assume by "topics" you mean "titles" such as you would use for an essay or as a header for a discussion topic. As such, you do not need a complete sentence, but you want the most efficient and succinct way to describe the idea of your topic: "Why Diamonds are Expensive" is more succint and also clearer in meaning. Your second example bothers me because the verb choice is a little vague. Do you mean "Where to Find Diamonds" or perhaps "Where Diamonds are Born"? The latter would be intentionally metaphorical, of course.
2. No, past tense won't work there. Try one of the following:
I hope she eats her lunch. (I want her to eat her lunch, but maybe she won't)
I hope she will eat her lunch. (Same as above, more distinctly in the future)
I hope she has eaten her lunch. (She should have eaten her lunch already; maybe now she won't be able to.)
I wish she would eat her lunch. (She's not eating it, and I think she should.)
I wish she had eaten her lunch. (She didn't eat it, and I think she should have.)
I wish she would have eaten her lunch. (Same as above.)
I wish her to eat her lunch. (Or) I wish for her to eat her lunch. (It is my desire that she will eat her lunch.)
Note: Wish and hope are not interchangeable in the above sentences.
- For Teachers