I'm playing 1.3 from your installer- not using 7th Heaven.
That's very strange. I made changes there and tested them; I guess I missed something?
Status Report
-) Talking to Cloud as Cloud in his house (...): Should be fixed, I imported a default field screen and ran around in there.
-) Vanishing Tifa in her house: She appears to be visible on Disc 2 & 3 in my game; not sure what could have happened.
-) Icicle Inn Thing: I'm doing two things here; first, I'm restoring the handler that prevents Tifa and Cid from going down to the Great Glacier while Cloud isn't in the party. The second thing is setting up the big ice helter-skelter (the one that lets you leave Great Glacier immediately) so that it drops you inside Icicle Inn instead.
-) Spell Order: This has been fixed; I found a set-up that's not too disorganised and which uses the original's numbering. One oddity I learned about the default game is that while the game lists three types of magic, it actually groups them into four. The fourth group is the 'extreme' magic, Contain, Ultima, FullCure, Comet/Comet2, and Shield. No matter what spell order you pick, these remain at the bottom. What I'd tried to do with the previous patch was place these spells in the three groups that are moved around (Attack, Restore, and Indirect) which is what likely caused some spells to vanish with certain configurations. I've learned my lesson and put them back to how they were
-) Keycard Fiasco: While it's possible to progress through here as-is, it's confusing as all hell so I've made the following change.
When heading up through Shinra HQ, Air Buster now gives Keycard 66 AND 68. This unlocks the doors for the stairwell. I've also added the handler for the elevator so that can be used too.
When defeating Hojo on Floor 68 (he's in the specimen container where Sample HO512 is fought), Floor 69 is unlocked. Unfortunately, there's no actual key-item called Keycard 69 so instead I've added a message and chime informing the player that all floors have been unlocked. That should take care of it.