R.1) In the UK, vagrants asking for change are ubiquitous. I'm interested in the oft-heard sentences they say: some say "spare some change, please"; some say "spare any change, please". In formal grammar, any is only used in question/negative statements but we all know that's all 'too dead in books' and not applicable in real life; therefore, some is possible here. However, are both of them really correct? Are there any differences in meaning?
Both are correct. But your logic is bad. The notion that " 'any' is only used in question/negative statements" does not mean that 'some', or any other word, can't be used in question/negative statements. It means that 'any' can't be used in positive phrases.
What does "too dead in books" mean?
2) I don't know
3) Last, I don't quite understand what this sentence means.
"WE have your best intention in mind"
Does it mean, we know full well what your want, implying that we'll do our best for your interest?
It's probably wrong. I think it should be, "We have your best interests in mind". "Best intention" isn't a common phrase. More context is needed to explain the sentence if there is no error in it.
Very Many Thanks!
Student or Learner