Are these units in common usage in Romania(n)? These topics have many seemingly obscure words, at least from English
No, but they are taught in highschool, and I assume most of the contributors are young people. We do use hectares to measure land areas, 'un hectar - două hectare'.
The final “i” of “hectolitri” in the audio sounds as clear as if it were “hectolitrii” (definite article). Is this a special phonetic situation? Maybe because of the consonant cluster “tr” at the end of the word?
Yes, this is a special case, because the singular ends in 'u' (litru). The final 'i' is fully pronounced, like English 'ee'.