Shou 님은 답변을 하지 않고 글을 수정해 주신 것 같네요.
1) "commonly/regularly"을 (예를 들면, 일상 대화에) 말하고 싶으면 어느 부사를 사용할 수 있나요? 흔하게, 일반적으로, 보통, 아니면 다른 단어?
The answer for number one is this:
You can use all the ones that you gave as the examples for it. The Korean speakers will get the message. Nice job! But to add, (because there are always more!) you can also use 많이 as well, which means "a lot."
2) 몇 부사를 함게 어떻게 사용하나요?
You are wondering how in Korean you can write phrases such as "He exercised often and diligently" kind of sentences aren't you?
For the example I gave above, it would be 그는 자주 열심히 운동했다. As you can see, the two adverbs just come right after another. Then you would wonder, am I allowed to switch the two adverbs' spots? The answer is yes. But I would recommend you to place the adverb that has a shorter spelling to be in the front.
If you want to ramp up the complexity,You can also say it like 그는 자주, (또한/또) 열심히 운동했다. Which is in English, "He exercised often, as well as diligently."
What you said is basically right, and will get the message to the other,but needs a little fix to: 이 표현이 일반적, (또/또한) 자연적으로 사용되나요?