I'd love FF7's magic system to be fixed such as what natepley suggests, I have a much simpler idea to give the gamer materia though.
my Idea is to give materia at the end of boss fights, so you can get esuna after a boss fight as an example, for the cases of bolt2 well the gamer would simply unequip their bolt1 for bolt2, its not too unlike ff8 where you can move level 2 magic to people and remove level 1 magic from others, something like this only happens at a few points in the whole game, its likely you will get fire2/bolt2/ice2/Quake2 all at the same time, I would also suggest everyone getting 3 of each.
A materia like life2 is something you can get after defeating aerith mime in the new threat boss, that way defeating bosses would be really cool as you get materia that really makes a difference,whereas vanilla ff7 was really crap in that you got life2 by just equiping life as soon as possible and just leveling up the materia which is just a boring way to give you awesome materia.
for materia like 2x cut that can come from maybe the last new threat boss, I think there should be only 1 materia like that and you can't level it to 4x cut, but I'll make that your decision, I don't even know where 2x cut is in your NT mod.
but yeah doing this would make the game WAY better, possibly the best final fantasy magic obtaining system to date.
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I don't see the point in movie/music player, I'd never use it, but I wouldn't be bothered if it was there or not.
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an FF9 auction, not sure on that, overall I would prefer the whole money system was rebalanced better, maybe it should be discarded entirely, or used only for the auction? and in that case shops sell items for free, because things are soo cheap in final fantasy they might as well be free.
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I don't know what you mean by replaying the date scene, would you get another boss fight, and how would this play into the story, well i think fighting a boss fight it that play thing would be cool, but a battle map would have to be made.
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finding the save points seems useless, but I guess some people like that kind of thing.
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another cool thing could be to have midgar zolom as a new threat boss, in this case he wont eject you out of battle, he can also give you cool materia, I don't know how midgar zolom is scaled in NT mod, I never went back to try to defeat him later in the game.