I enable and setup the SMTP to SMS (the status of pop3 is Running (Polling pop3 mailbox), and sent several email to that pop3 mail box. After several minutes, I still can't find email in the inbox of that pop3 account. I checked Mysql database, I can't find the data in smsoutgoing table as well.
Question 1: will ActiveSMS retrieve any email from pop3 server, in result, any other email browser can't review the email later.
Question 2: why can't I find data in smsoutgoing table
Question 3: Why can't I receive SMS? I test sending SMS via ActiveSMS test, it works fine. I use default mobile phone number rule (in subject, replace 0 by 86)

Question 1: will ActiveSMS retrieve any email from pop3 server, in result, any other email browser can't review the email later?

ActiveSMS removes messages from the POP3 mailbox after they have been sent.

Question 2: why can't I find data in smsoutgoing table?

The SMSOutgoing table only contains message they are queued to be sent. Once a message is sent it will be removed from the SMSOutgoing table (all but the last one).

ActiveSMS does have a message Logging Feature, this can be setup on the Loggin tab of the ActiveSMS Console.

Question 3: Why can't I receive SMS? I test sending SMS via ActiveSMS test, it works fine. I use default mobile phone number rule (in subject, replace 0 by 86)?

To enable us to resolve this issue could you please turn-on trace logging.

To turn-on email gateway trace logging you need to do the following:-
http://www.intellisoftwa...SMS_EmailGWEnableLog.zip 
2. Extract the ActiveSMS_EmailGWEnableLog_ON.reg file
3. Double click on the ActiveSMS_EmailGWEnableLog_ON.reg file and select Yes to accept changes
4. Goto 'Start Menu->Settings->Control Panel->Administrative Tools', double-click on 'Services'.
5. Double-click on 'ActiveSMS Email Gateway', and click 'Stop' and then 'Start'

Run a short test to re-create the problem. Once the test complete,
please email the log files listed below to mailto:support@intellisoftware.co.uk

C:\ActiveSMSEmailGWIncomingLog.txt
C:\ActiveSMSEmailGWOutgoingLog.txt

To turn off logging extract and double-click on the ActiveSMS_EmailGWEnableLog_OFF.reg file.