Q: I’m dealing with power. とはどういう意味ですか?
A: It is not clear without more information. It might mean that the person is having problems with their electricity.
Q: so how you doing ? I’m dealing. とはどういう意味ですか?
A: So how you doing? is the same as How are you doing? but its more casual. dealing might mean that the person might not be happy but they are doing the best they can.
Q: I hope you understand that i’m dealing とはどういう意味ですか?
A: I am not sure I know exactly what you mean, but in America, "dealing" means working through a problem while trying to keep life normal. To me your sentence means, "Please understand that I seem to be OK, but I am privately working through some problems."


Q: I missed what she said as I got busy dealing with the new wave of emotion that flooded me. I felt like my heart has been shoved and tears clouded my vision as everything I heard slowly sank in.

Is it wrong?
A: Not in any way. It's well stated.
Q: I am busy dealing with the issue of coronavirus these days. この表現は自然ですか?
A: I am busy dealing with the coronavirus issue these days.
Q: I’m dealing with the customer right now. この表現は自然ですか?
A: I think the word “dealing” can be rude when talking about someone else. It makes it sound like you are unhappy with the customer, or the customer is being rude to you. I would say “I’m helping a customer right now.”
Q: It was tiring dealing with customer who try to nonstop talk to me. この表現は自然ですか?
A: It was (a pain/a nuisance/tiring) dealing with a customer who kept trying to talk to me non-stop.
Q: I'm busy dealing with my graduation recently. この表現は自然ですか?
A: Your sentence is good if you are explaining why you cannot do something. However, if you are simply talking about your life, I would prefer: "I have been busy dealing with my graduation recently."