For English speakers, is it possible to say "Dinner will be served about (or around) seven." without saying "at" ?

About or around mean that it will be served at approximately seven, whereas if you use 'at' it means more exactly. You would not  normally use 'at' and either 'about' or 'around' together'

Yes, it's possible.  If you use "around", you would drop the "at".  Etiquette-wise, this is something you'd SAY (verbally) or WRITE in a note, rather than something you'd print on an invitation.  (The phrase "dinner will be served" is a formal-sounding structure, which automatically leads native-speakers to assume you're proposing a printed invitation, as opposed to just leaving someone a sticky-note or a voice-mail.)

On a printed dinner invitation, it's customary to state a specific time even though both the sender and the recipient understand that time to be only a target, and in actuality the event might begin somewhat earlier or later.  Printed invitations have their own layout conventions, which avoid such verbiage issues.  Your stationer can advise you, if that's what you're considering.

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Yes, but it's not proper. People know that such designations are always approximate.

You might say it, but you wouldn't write it that way. 

Those are all awkward.

I might say, "Dinner will be served at seven." or "Dinner will be served by seven."

PS - If a number is less than ten (10) - use the word, not the numeral. As for time, that usually extends to eleven and twelve.