Hello, I think I have figured out the problem. I am sharing it in case anyone may have the same problem in the future.
In short, I bought a host service in Godaddy, and get my Joomla installed with their auto installation tool, which makes the email address of Site Admin look like this: "devnull@installatron.com". All the emails sending from the site are from this address.
However, this address is different from the "Custom Email Address" which I put in "Send Request to" in 2paypal. My gmail just can't get the request email. Don't know why.
However, after I changed "devnull@installatron.com" to a Gmail address which is the same what I put in the 2paypal, I got the request email right away, though with a warning of security.