Unfortunately I don't know (or at least: can't remember ) how Cubase's generic remote works, so I can't offer any concrete advice on that.
(Does Cubase automatically upload its own preset to the BCR, or must the user select a particular standard BCR preset manually?)

In any case, it may help to realize that the BCR has 32 memory presets plus one temporary preset.
The temporary preset determines how the BCR behaves at all times.
Whenever a memory preset becomes active (e.g. when you select it by pressing the PRESET < or > key on the BCR), the definition of that memory preset gets copied to the temporary preset.
When you change the definition of a button or encoder (e.g. via the EDIT button on the BCR), it's only the temporary preset that gets changed. So whenever you switch to a memory preset, any unsaved changes to the temporary preset get lost.
The only way to save changes made to the temporary preset is by performing a "store" operation: this copies the temporary preset to a memory preset of your choice. Maybe that's what you did accidentally by pressing the STORE button?
If you're uncertain about the contents of your BCR's memory presets, you can run BC Manager's "Receive all data" operation from the "B-Controls" window.

Is there a default reset to default seting on the BCR?

The BCR doesn't have an inbuilt "restore factory presets" operation, if that's what you mean.
You have to restore any memory presets manually. Again you can use BC Manager for this: load the syx file containing the desired preset into BC Manager, then upload it to the BCR.

Behringer took down their BCF/BCR2000 support pages about a year ago, and I'm not sure whether you can still find Behringer's own standard preset collection anywhere else on the internet. If you indeed need one of these standard Behringer presets and can't find them anywhere, I'll consider making them available via the "B-Control user files" area at this website.

Hope this helps,
   Mark.