Is “duh” a common exclamation?

In what situation can I use "but the thing is"?

"The thing is" is used to introduce an explanation or to give an excuse for something. It can also be used simply to emphasize a point. Ex: A: Let's go to the pool! B: Yeah but the thing is, I don't know how to swim. Ex: We can drive downtown but the thing is, most of the shops are closed now.

Can I replace "part of" with "one of" here? What is the difference between "one of" and "part of"?

Yes, in this context you can replace "part of the reason for this" with "one of the reasons for this". However, these two expressions are not always interchangeable. "Part of the reason" is usually used when there is one reason for something happening, and someone is explaining part of this one reason. "One of the reasons" is used when there are multiple reasons for something occurring and they can be listed. In this case, however, he uses "part of the reason" to have the same meaning as "one of the reasons" since he gives multiple reasons.

What does "big time" mean here?

"The big time" is an informal noun meaning the highest or most successful level in a career, and it's usually used to mean Hollywood (the film industry). This is what the speaker is referring to here. Ex: She didn't want to play small shows anymore. She was ready for the big time. Ex: The singer shot to the top of the charts as soon as she debuted. It didn't take long for her to make the big time.

What does "crystal clear" mean? and how can I use it?

When someone says something is "crystal clear" it means that they completely understand a situation or statement. It can also mean that something is very obvious. That there is no confusion at all. Ex: It's crystal clear that he's the one in charge. Ex: The citizens have made it crystal clear that they don't want the new highway built.

Is “duh” a common exclamation?

"Duh" was more common in the early 2000s, but now is only used sarcastically because it is considered somewhat rude to say. Right now, young people (mostly teenagers) only use "duh" when the person they are speaking to clearly knows they are joking. "Duh" should not be used in formal situations. Ex: Of course I am the coolest person ever. Duh! Ex: Duh my favorite color is black! Can't you see that everything I own is black?