Should it be allowed to ask for religious text e.g. Text of the condolence which is given to Muhammad(saww) on the Day of Ashura?, which is available in religious books but not available over the internet, along with the translation and possibly the transliteration as well?
In general, I don't see a problem with this. It mostly sounds like a case of source-identification, which is to say you are searching for a particular and specific reference, rather than a vague "Are there any dua for..." (which would effectively just be a list question).
In other words, it's objectively answerable. You're not seeking items, or ideas, or opinions, you're seeking an answer, and you know (or reasonably suspect) that there is an existing text out there which does answer your question.
As long as the question itself is good (i.e. not just an excuse to copy-paste text verbatim from a third-party), the requested source being online or offline shouldn't make a difference (although, under the principle of Making the Internet a Better Place, I'd love to see more offline-specific requests since that information is otherwise so difficult to find online).
Whether the question and requested source is any good (which is to say useful) would have to be left up to community voting; even if we wanted to, I doubt we could really set any hard and fast rules on what is, and is not, useful to the community. Like any question, the onus is still on the questioner to prove its value.