Well, if it really doesn't work with phpbb forum, then I guess phpbb sucks, I browsed around their code and I really didn't anything good in the coding.. anyway, why not use the simple function mail() for a phpbb forum, let it send the email through it, you don't really need a smpt server to send your emails from the phpbb.. Well, maybe some servers have some limits with mail() then just get a better server without those limits and don't use phpbb?

I guess the reason why when sending email through Google SMPT server the reply email is your gmail account email is logical, I would also do that if I was Google.. Why not just create a separate Gmail account with for example my-super-useless-website-phpbb-mail @ gmail.com and use it for things like that? ;]

Besides, google isn't the only service which is offering a SMPT to send your emails, I guess there are much more services like that for free or paid and usually your ISP has a SMPT server which I guess is much faster for you!

I can never connect with Google Mail via SMTP. I did not know why. I am sure I have set the SMTP server on. The port is set as 110 port.

Yes if you have a gmail email account then you can route emails through their smtp server using your account username and password. But make certain that your intentions are good because google has an excellent spam filter.