Yes, writing of diaries was not encouraged but many soldiers (mostly officers with access to paper, time and privacy) still kept them despite the ban.

"Penalty of death" claim is overblown. There is no known official order about such thing. However, some political officers were claiming it was "ordered by Stalin", but I think mostly to scare troops from keeping diary:

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Комиссар роты, которой командовал Черниловский, увидев у него записную книжку, отобрал ее и бросил в печурку: «Помни, комроты, товарищ Сталин приказал: всех, кто будет вести дневники, – расстреливать». «Не знаю, был ли такой приказ, но дневников я больше не вел. Как и все», – писал Черниловский более полувека спустя

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Chernilovsky didn't suffer any further consequences (other then burnt notebook). Sgt (later Lt) Gelfand kept diary which was sort of "curated" by political officer.

Pawel Elkinson (artillery scout) kept diary from Aug 1944 to May 1, 1945 - here's a scan - see [1]

Yes, several war-time diaries were published. I do not know whether any of them were translated into English.

Source

1. Jews at war Article about soviet jewish soldiers and officers who kept diaries, with scans of a diary.