運命を信じる？って英語でなんて言うの？

Most people use fate and destiny interchangeably, but they aren’t the same. Fate is the life you lead if you never put yourself in the path of greatness. That’s the direction your life moves in without any effort on your part. That’s your fate. Fate is a negative and is defined as the expected result of normal development. Normal development. Never taking a risk is your inevitable fate. "Is your fate to never leave that cruel husband of yours?" Destiny is your potential waiting to happen. It’s the top tier in the grand scheme of possibilities and where your dreams come true. You have to be willing to take that first step to reach your potential, even if it’s a risk. With great risk comes great failure. Let’s flip that phrase around. With great risk comes great reward. Ultimately, that means there’s no greater risk than no risk at all. "Do you believe our future is predetermined?"

Any of these is a correct way to ask someone if they believe if their life and others lives are predetermined.

Do you believe in destiny? This is quite direct. You are asking if the person does believe that everyone's future is predetermined and cannot be changed. In the second question, you are asking if one's fate is 'cast in stone', i.e., it can never be changed whatsoever. In the third question, you are asking if the person believes that one's future is already determined by a supernatural power such as God's power and it cannot be changed.

examples "Do you believe everything happens for a reason?" or "Do you believe in fate?" or "Do you believe in destiny?"

"Do you believe in karma" "Do you believe in fortune" You could use the synonyms "karma" and "fortune" to ask people if they believe in destiny or fate. Destiny is a predetermined course of events be it good or bad "karma".