Several compilers have recently been using the word 'regularly' to mean every other letter of a word. So nut is formed from the regular letters of insult.
25 ac is exotica (ex for old, then anagram of a coat)
Sorry - forgot about 23 down. Answer is Niobe - daughter of Tantalus who wept for her slain children, was turned into stone and the stone continued to weep!
25ac Ex(old) otica (coat i replaced) = exotica
23d N (new) i (one) obe (order of the British Empire) = Niobe her children were killed and she was turned to stone after annoying the Gods Apollo & Diana