It would be better to say "I had thought that for having moved from the US, things would have changed." By saying "would have changed," you're using the past perfect conditional tense, which matches with the past perfect "had thought" that's used in the beginning of the sentence. With complex sentences that have multiple verb clauses, it's very frequently necessary to match the verb tenses together.

There are several steps you should take to plan your speech. 1. What is globalization? Read about it online or in your textbook. Once you understand what it means, think about: 2. How can parents teach the values of globalization to their children at home? When we say something "begins at home," it usually means parents teach it to their children while they're young. So how can this be done in terms of globalization? 3. Plan! Create an outline. Start by writing three main points about how parents can teach children about globalization. Then add some supporting details, examples, and/or steps for each main idea. Whatever you do, DON'T copy from a book or website; make sure these ideas are in your own words and from your mind! Also make sure you're following the assignment structure for the speech. 4. Practice! Say the speech a few times by yourself until it becomes comfortable. Time yourself to make sure it's within the time limits. Make changes if you need to. You can even record a video to watch it and find mistakes. When you feel comfortable, you're ready! Good luck!

These phrases are a little context dependent, but the short answer is no, they have slightly different meanings. "In the city" is a little more broad - it refers to any object that exists, or action that happens within the area of the city. "Across the city" is a little more specific - it either means something that exists on the other side of the city (Example - Her house is all the way across the city) or that a continuous action happens while traveling from one side of the city to the other (example: He drove across the city/The group has been performing across the city). Given that one is more broad and the other is more specific, there are some situations where the meaning could overlap. Example: They performed in the city all year long vs. They performed across the city all year long. Even though the meanings are a little different in general, in this situation they overlap.

"Legacy" is often used to talk about the lasting impact that something has on society, as is the case here. So instead you could say impact, importance, relevance, etc.

May and might are very similar, but can be used in some different situations. For example, when asking for permission ("May I do something?") We only use may. When talking about future possibilities ("I might do it tomorrow" vs "I may do it tomorrow") it's used in the same way. Some people will tell you that "might" has a higher chance of happening than "may" (something like 50% vs 40% respectively) but not all native speakers will agree.

What you can do to prepare depends on which section you're preparing for. Beyond expanding your vocabulary and reviewing grammar, for the IELTS speaking exam. you can watch example videos showing people who reached the score you're aiming for. Then record yourself responding to some example questions, watch the video and compare. An italki teacher with experience with the IELTS would also be able to give you some feedback. Preparing for the writing section would be similar. Read several example essays that reach the score you're aiming for. Set a timer and write an essay using a practice prompt, and compare. For listening and reading, the main thing is to expand your vocabulary and test taking skills, watch videos and read articles online for practice, and then do as many practice exams as you can. Your score will gradually improve.