Is there any evidence that the length of the beard is a fistful, and is the hadith "Whoever trims his beard shorter than a fistful, Allah shall blacken his face on the Day of Resurrection" authentic, and what is its chain of narration and ruling?

Keeping the beard and letting it grow is a Sunnah, and shaving it is Haram (forbidden) and impermissible according to the majority of scholars. Scholars have allowed taking what exceeds a fistful of it, based on what was reported from Ibn 'Umar and Abu Hurairah that they used to do so. As for the speech or Hadith you mentioned, there is no basis for it in the books of Hadith.