Literally, 현대 means 'modern times'. It's Romanized as 'Hyundai' with -ai because that is a remnant of an older transliteration system -- the vowel ㅐ is comprised of ㅏ + ㅣ(a + i), so even though it isn't pronounced as a diphthong and sounds nothing like the vowels it's comprised of, that's the origin of the spelling.
Because that's a nonsense word that doesn't mean anything. Hyundai is an actual corporation that is spelled 현대 in Hangeul. It doesn't follow the standard transliteration rule because it predates the Revised Romanization system that you are following.