I airmailed it to you last week, and I believe you should be receiving it soon. - is the word "airmailed" used correctly here? Yes. is it fine to use "post"? (Yes, it is more British and American) which one is more common? Airmail is a specific type of mailing. - "should be receiving" used correctly here? Yes, it means that I
1)"I airmailed it to you last week, and I believe that you receive it soon" No
2)"I airmailed it to you last week, and I believe you to receive it soon"No 3)"I airmailed it to you last week, and I believe you'll receive it soon" OK.
You're very helpful, and your explanation is very clear. I love English and this is a very good way for me to learn in my everyday life. Thanks, AlpheccaStars!