When praying fard, is it allowed for one long surah be used for both of the raka'at?
e.g. Praying ayahs 1-15 of surah mulk for the first raka'at and then continuing for ayahs 16-30 of surah mulk
Yes. Imams often and regularly break up surat similarly when reciting in tarawih.
Generally, only al-Fatihah is considered strictly necessary when reciting fard salat; beyond that you may recite from the Qur'an however is easy for you.
To my knowledge, the general ruling for any recitation after al-Fatihah is that it should be at least three ayat, but there's no requirement that this recitation needs make up a complete surah.