Can a phrophecies only account participate in the War in Kryta?

By having someone run you through or something?

EN is mandatory for the Trial of Zinn. You can't enter the Tower and get the missions without it.

The spawns in explorable areas are activated anyway, so you'll get only partial access to WiK.

No.
Also, theres no way to run through any part of the WiK content.

no chance.. you MUST have EoTN because part of the storyline revolves around Gwen and Keirnan Thackary... and you MUST have completed either Proph or EoTN before you can get the WiK stuff. RTFM lol..

Not really, their part of the storyline is entirely optional.

If you choose not to follow the dialogues between Keiran and Gwen in the HoM and don't help him with the organization of her birthday party, the Ebon Falcons simply don't take part in the War, while Keiran and Langmar only appear during the "Mustering a Response" quest.

The only reason why EoTN is mandatory is actually the Trial of Zinn, required to gain access to the Lion's Arch Keep, together with the first 3 dialogues at the Shining Blade War Camp.

So, the furthest a Prophecies only account can get is the first three dialogues in the Talmark wilderness. The fourth already stops due to not having Zinn's task done.

However you can get the trial of Zinn without EotN. You just need to complete Zinn's task. Of course you need all three campaigns to do this.

No, completing Zinn's task is a substitute for completing EotN. You still then need EotN to access the Trial of Zinn from Arbor Bay.

You can unlock it by just completing Zinn's Task. Still, without EoTN, you just cannot attend it, as you lack access to Vlox's Falls.