Hello! Thank you for your question. The second sentence is correct: "What is the initial deposit to open a bank account at your bank?" However, you could also say, "How much is the initial deposit to open a bank account at your bank?"

Hello! This would be how an American would write this sentence: "If I don't text you for a while, it doesn't mean that I forgot about you. You are always in my thoughts and my heart." NOTE: Keep in mind that this is an informal sentence. This is how those in the U.S. would speak, text, or write an informal email to a friend. (By the way, your sentences are a beautiful way to explain this situation. Great job!)

Yes, the sentence is grammatically correct and also makes sense. I only have one comment for you: This is a very passive sentence. It is definitely not the way an American English speaker would speak. Americans also try not to write passively, unless there is a particular reason. We would tend to SPEAK sentences like..."I need to replace that light bulb so I can see better in this room." OR "The last light bulb just went out. Now it's completely dark in this room." If an American were to WRITE this sentence, we may write the following: "We use light bulbs to provide light to dark areas so we can see."

I agree with the rewording of the sentence to...Every time I climb the stairs, I stumble and fall. (You do not need the word "up" because you have already said you are climbing, which implies "up.")

However, the "do or die" sentence is out of place here. I would delete it completely . "It's do or die" is used in very serious situations. It's used in movies, but not typically in American English conversation.

In movies, a superhero may say...I have to save the city at any cost. It's do or die. Wish me luck." The superhero is saying that he will save the city or die trying.

This is passive language and likely poor writing. In reviews, you want to write in the first person. Whatever the reason, it is the same as saying, "I felt that..." The person felt like going to this location would give them good opportunities to learn certain art.

The word "up" is not needed, but people from the U.S. often use it in this way It means that the person lives south of Maine. So, to travel to Maine, they must go north or "up." This is important for understanding American English, but you do not need to use it in your speaking