Translation:We would not publish your contribution.
Separable. Actually, it is recommended to always separate it.
bekannt machen - alternatively bekanntmachen.
be- by itself is always an inseparable prefix, though.
„Veröffentlicht „ is the past participle, like published in English. You use it for perfect or Plusquamperfekt tenses with haben as the conjugated auxiliary verb.
Ich habe veröffentlicht.
I have published.
Ich hatte veröffentlicht.
I had published.
(Also futur II)
The Infinitiv veröffentlichen is used similarly to English „to publish“.
Ich würde veröffentlichen. I would publish.
Conditional with würde/would
Yes it could. However, the default meaning for “Beitrag veröffentlichen” for me would be “publish the article”. Beitrag could be a little less ambitious than article like “your bit” or “your letter to the editor”. However, Beitrag is also what is mostly used for television, but then it would rather be “Beitrag senden” broadcast your bit.