The answer from @kimeo is a very good one to the portion of the question related to UK defamation liability for a not expressly identified subject. I'll expand in this answer on a couple of other aspects of the question.
What about specific, public accusations ("this person was killed by
such and such means"), but with the perpetrator only vaguely
specified?
There are different ways this could be false, and different consequences. If the person was not killed and the claimed means by which the person was killed (e.g. imagine an embarrassing scenario involving a sex toy) would tend to damage the reputation of the person allegedly killed, the person allegedly killed might very well have a defamation claim against the person making the statement.
Dead people can't sue for defamation, however.
And if the claimed means of death were wrong but innocuous (e.g. the claim is that they were killed in a car crash that actually just seriously injured them, when they really suffered their injury in a slip and fall incident), there would be no basis for a defamation lawsuit.
False statements are not always a basis for legal action, particularly if the matter about which they are false is not material in context.
In the same vein, if someone says, "Sue is from Cornwall" and Sue is actually from Bath and has never even set foot in Cornwall and the speaker knows that fact, in all likelihood this isn't a falsehood with legal consequences in a defamation action.
Like "someone in my extended family killed their parent, but I don't
have solid evidence / Police refused to investigate"? What if,
further, one provides some little detail, which narrows it down to a
small few accused persons?
Assuming that the parent died, and that the police indeed do refuse to investigate, I'm not certain that this would be an actionable on any basis.
While the initial statement X killed Y is facially defamatory if the identification of X is sufficient to determine who was being talked about, by saying "I don't have solid evidence" the child of the deceased parent is qualifying the statement about the alleged killer and essentially saying that even though his initial statement sounds like one of fact, he is actually really just saying that he has unsubstantiated suspicions that X killed Y, when you take the entire statement as a whole.
Unlike that unqualified statement that X killed Y, which would be defamatory if false or without any real basis for knowing that this is true or false, I am not at all convinced that once you disclose that you have a mere suspicion not backed up by any evidence in the same utterance, that the statement continues to be defamatory. You do indeed have a suspicion not backed up by evidence, so to that extent it is true. You aren't claiming to have more.