Willer Express

I am studying in Japan. I want to use Willer expres. Is it possible to request some of my friend staying outside japan to buy pass for me so that I can use it. Because one cannot buy it from inside Japan.

Is it possible to request some of my friend staying outside japan to buy pass for me so that I can use it

It seems not.

In the following webpage, it is stated that "the pass can only be used by the person to whom it is issued."
- http://willerexpress.com/x/bus/dynamic/3/en/html/pc/buspass/index_ja.h...

If your friend buys a Japan Bus Pass, the pass is considered to be issued to that friend, not to you.

If I buy a willer express pass while I am in my country, can I use it after I come back to Japan within two months?

In answer to your original question, I found this on the Willer website's bus pass FAQ:

http://willerexpress.com/x/bus/dynamic/3/en/html/pc/info/inquiry/qa/an...

"Can I purchase a Bus Pass on behalf of my friend?

As long as you and your friend will travel the same routes, you can purchase a pass for your friend from your MY PAGE.
However, if you and your friend are planning to travel different routes, your friend has to buy one on their own."

Regarding your follow up question, I don't see any reason why you couldn't buy the pass in your country and then use it in Japan. Indeed, it seems that even a Japanese national and resident could simply leave Japan, buy the pass, then use it in Japan.

As a matter of interest, what actually stops you from buying this in Japan? I've never purchased one myself, but it seems that there is no physical ticket, so presumably they don't require a non-Japanese address for postage. Surely it's not done on an IP Address Basis? In that case you could just use a proxy server (although that would, of course, be completely illegal and I certainly don't condone it).

Anyway, I hope this answers your question.