You can say,

1. “Hope you are doing well and safe.”
2. “Hope your day is going well.”
3. “It’s a pleasure to meet you.”
4. “Good morning/afternoon/evening.”
5. “May I ask how are you?”
6. “How’s everything?”
7. “Is there anything I can help you with?”
8. “Are you feeling any better?”
9. “Would you like to join me for tea/coffee/drink?”
10. “Thank you for taking the time to talk to me.”

You can say,

1. I’m sorry about {insert problem here}. I’m talking with my team about exploring this issue more now. I just want to let you know that your issue is important to us, and we’ll get back to you ASAP with proper insight and solutions. Thanks for your patience,{name}
2. An apology can be a simple statement, or it can be a more elaborate explanation of the problem. If the mistake was a typo, then you can simply say “I’m sorry for the inconvenience.”
3. If it’s something more serious, it can be helpful to explain the situation, but also why you are apologizing. For example, if you accidentally deleted all of your client’s data and their files are on a server that they can’t access, then you could say something like: I’m sorry about this. It was an unfortunate situation. The reason I’m apologizing is because it was unintentional and I didn’t realize that I had done it.
4. You can always add “Thank you for trusting me with your business” as a nice touch to show you’re grateful for the client’s time and trust. If you’re unsure how to write an apology, it may be worth talking to your boss or mentor, or maybe a friend who’s good at writing emails.