Sorry this got a little long...
I am self-studying a course. Two years ago I began to use some lectures by a professor from the United States (I'm from a different country). He is retired now. While watching his lectures, I began to have some questions about the topics. So I usually sent him an email which he usually replies to quickly. This has been going for a long time and I am extremely grateful that he almost always found time to answer my questions and even answer my follow up questions.
Last month, I sent him an email. He didn't respond. This is perfectly understandable because he might be very busy. The next day I sent him another email asking another question, and he responded to wait for a week before he can answer me because he has been very busy. I'm pretty ashamed at this point because I'm not sure if I am annoying him already.
Finally, yesterday I thought he is no longer busy, I sent him an email to ask another question. He responded something like this (not exact words):
Sorry it looks like I am ignoring you. I have been very busy and answering your questions isn't a small amount of time.
Then proceeds to answer my question and asked if I understood.
Now I began to panic because he felt that he is ignoring me. The thing is I don't feel ignored at all. I know he's busy. In fact when I first started sending emails my hope is he would reply just a few times. I never expected he would help me a lot by always replying to my emails.
So my question is: how can I tell this professor that I don't feel ignore by him because I know he can be very busy and just answer my questions if he has the time? And also, if it matters, how can I express that I am extremely grateful he even answers my questions at all? I am not even one of his students. I just know about him through his lecture videos.
I am not sure what to do because I don't know the culture of the United States and I might offend him somehow by replying rashly. This professor has been very kind to me, and I do not wish to do something that might offend him.