1. The dialogue/text from Areios. Is that supposed to be corresponding to the Japanese voice lines in the game? As in English dialogue on screen while the Japanese voice lines play during gameplay?
Yes, that's the point of adding subtitles. Since we *still* don't have the English dub done, which would be the preferred alternative if it was high-quality, then adding subtitles seems like the best way to get this translation finally finished and released.
The line shown in that screenshot is *not* in the Japanese dialog from that particular scene, it's just a proof-of-concept test.
2. Was stuff like that (like in the picture for Areios? dialogue) ever in the original Japanese version? If not, was it just the Japanese voice lines with no subtitles or just text? That?s based on my understanding from looking at this picture.
No, the original game had no subtitles for the cutscenes, just voice acting ... which is rather the point of taking advantage of CD-ROM as a game-delivery media.
There are very few PC Engine CD games that have CD audio spoken dialog with simultaneous text display. Off the top of my head I can only think of "Anearth Fantasy Stories", but there may be others.
Hacking subtitles into an existing game is extremely difficult, but since it has been done before by "Supper" for one of his translations, it seems worth the effort to attempt to add subtitles to the LoX translations in order to get them releasable after all of these years.