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I think the confusion is with the newer keyboards that no longer have the MUSIC FINDER as my S950 has. It is a handy feature that Yamaha has done away with for some unknown reason.
With the SX keyboard you will be stuck with using the registration to call up your custom song styles. You might use Slot #1 to save the intro you will use for the song. Then use Slots #7 and #8 to hold your mic settings.
I dread getting the SX keyboard knowing the Music Finder is now missing from the keyboards. I may wind up simply putting my styes in 20 folders with 16 styles (songs) in each of them. Then just select the style I want and referred to my lead sheet as to how the song starts, with an intro or one of the mains. That way the registrations I would still only use for Mic settings and controlling the backup singers.
No, the status of the Freeze button cannot be saved in Registrations.
The purpose of the Freeze function is that the parameter group(s) previously set in the Freeze setting display (press "Direct Access > Freeze") can no longer be changed by Registrations, OTS or MIDI files. However, you can easily edit your registrations so that certain parameter groups are not changed when a registration is called up.
For example, if you don't want a particular registration to switch the current style, just re-memorize each registration button "back to itself", but with the Style box unticked (and at least with the Voice and Keyboard Harmony boxes ticked). Then re-save the bank.