There is no validity period as such - and indeed, in this current case, some MPs did write letters of no confidence very soon into the current Prime Minister's tenure. Sir Roger Gale, for instance, revealed in December 2021 that he had written a letter shortly after the Barnard Castle incident in 2020. If such a letter is not explicitly withdrawn by the MP, it remains valid.
It is generally expected that on the threshold of letters from 15% of the parliamentary party being reached, the chairman of the 1922 committee will check with those who have put letters in to confirm their intentions. Indeed, when Theresa May was close to the threshold in 2018, government ministers were thought to have put in 'decoy' letters, so that they would have an early warning of the threshold being reached when a confirmation call from Sir Graham Brady came through. However, there is no guarantee that this is the case.
Before Sir Graham's tenure as chairman of the committee, letters had to be renewed annually - according to The Independent:
Under Sir Graham, a no-confidence letter is held on file indefinitely once submitted, unless the author asks for it to be withdrawn. Previously, they would have had to renew their objection on an annual basis.
As for your other questions, it's not entirely clear, as the 1922 committee rules aren't fully public, but I believe that in the case of a change of 1922 committee leadership fresh letters would have to be written. The chair of the committee is supposed to be the only individual aware of the exact number of letters sent, and the letters are also meant to be addressed to the current chair. In the case of a party leader surviving a confidence vote, I believe fresh letters would also have to be written - not least because under the current committee rules, no new confidence vote may be held for a year.
I don't believe a general election would require fresh letters to be written, as there would be no change in the structure of the Conservative party itself, unless of course the chair of the committee or the party leader lost their seat in parliament.