Singing Mountain specifically is allowed because it is present in the game's data. It's in the ROM of Chrono Trigger.
Hidden Palace Zone is also accessible in the sound test for Sonic 2 with out any kind of hacking or digging necessary. It's in game.
For other tracks, such as something "written for the game and included on the OST," if it isn't in the game data anywhere, it's not fair game for remixing, and you should not try to submit a remix using that as source music.
Also, just as a note, when asking these kinds of questions, don't just ask in the general sense. If you have a specific example of a song you want to remix, you need to be explicit about it and tell us exactly what you're planning to do. Asking about hypothetical situations will only get you generalized answers. If we know the specific track in question, we can investigate its specific eligibility.
Also remember; this is Ask a Judge. If you're not a Judge (or a staff member with an official answer), don't answer the questions. OCR doesn't always necessarily do things based on precedent; standards and rules have evolved and changed. What was permissible years ago (in the context of submissions) is not necessarily permissible today, and vice versa. You can't always just look at remixes posted years ago and say "YUP IT'S OKAY!"
We make an effort to be consistent and up front about things like standards and source eligibility, but OCR is 10+ years old and is a living and growing website. Things can change, so be careful about assumptions and presumptions.