Create a post in a Google+ Community direct from Gmail

The posts are most likely in the queue for moderation. This the only way what you describe happens.

And no, my posts are not awaiting for approval. I've been in the community before and posted tons of stuff into it and all of them were able to be seen by the public.

This does not mean anything. Posts historically being visible does not mean your current posts are not getting queued for moderation. The only way to know for sure though is for you to ask the community moderators.

I believe Ring Central Fax will do what you want.

I actually called them up to answer this question and here's the answers I got:

1. While their site talks about attaching things to email and faxing them, they will fax the body of an email message (apparently as a / in lieu of a coversheet)
2. The account has an address whitelist
3. ... but the email addresses on that whitelist can apparently have pluses, equal signs and commas in with their letters. (I'm at a 92% confidence level in this information)
4. ... to match the whitelist they said they check the From Header for whitelist matching. I'm only about 80% confident in this part of the answer, as the "senior tech rep" on call literally seemed to have no idea what RFC 821 was, or how you find such a thing on the Internet. I was really hoping he'd transfer me to someone who knew, but no dice.

But, I think this information is correct (after also fighting with them on fax header vs email message header, which was a fun bit of translation / telephone too)

Ring Central mostly advertises its VOIP capabilities and the fax stuff is kind of hard to find, so I'm hoping you missed this in your survey of email to fax solutions.