what is my phone’s own e-mail address?

I just got my phone from au by kddi.
then i tried sending text messages to my sis.. but then i heard that i can't send messages without my own ezweb account. then how do i figure out what my email account is? Plus, is 'text message' called 'mail' in japan?
I don't get the concept of e-mailing between two phones..
thanks!

If you are trying to send a message to another AU phone (or Softbank phone), you can do it number-to-number, which is called SMS. It's only up to 128 characters or so.

If you want to be able to send to e-mail addresses on PC, or phone of other companies, then you need to sign up for ezweb address, which you need to set up after you get your phone.

If you don't have any English language manual, go to an AU shop and ask for help :)

I just got my phone from au by kddi.
then i tried sending text messages to my sis.. but then i heard that i can't send messages without my own ezweb account.

First things first, is your sister in Japan as well, or are you trying to text an phone outside of Japan? The following assumes she has a Japanese cellphone:

If you signed up for mail services then you already have an ezweb account. If not then you need to go to an au store to sign up for mail. There's something like a 300 yen registration charge. You'll be assigned an email address made of a random string of letters and numbers, but you can customize it to whatever you want later. There is usually a Japanese web app to do this, so have the au person or someone who can read Japanese help you with that. Or you could just leave the address as it is, which will help prevent spam.

You don't actually need to know your own email address unless you need to tell it to someone, but one way to find out would be to send a mail to yourself (at a different address, like a computer account) and see where the mail came from.

To send a mail, open the mail program, and write an email as you would usually write an email on the computer, i.e. fill in the to field with your sister's phone email address, subject line with the subject, and the body with your message. Hit send when you're done.

I don't get the concept of e-mailing between two phones..

Just think of your phone as a small computer. Each phone has its own email address and mailing someones phone email address will send the message to their phone. You can also email regular computer email addresses from your phone.

Au phones also have a feature called c-mail that is more like an sms. Its not very useful though unless you will be sending short messages to other au phones.

Plus, is 'text message' called 'mail' in japan?

Yes

Does it cost the same to send an email to my hotmail account and to my friend's phone? I monthly pay about 2500 yen.. so approximately how many e-mails can i send a month?
btw, receiving mails either from hotmail account or cell phone account is free, isn't it?

Does it cost the same to send an email to my hotmail account and to my friend's phone?

Yes, it depends on your plan, but to send or receive mail you pay about .1 yen/packet and a typical text only mail is only a few packets.

I monthly pay about 2500 yen.. so approximately how many e-mails can i send a month?

You can send as many as you want, but of course you pay for however much data you use. Again that depends on your plan as there are unlimited mail plans available.

btw, receiving mails either from hotmail account or cell phone account is free, isn't it?

No, you pay the same rate to send AND receive mail. Both cellphone and computer based email is charged the same however.