For example, the ten GROBs, I understand, are lost on switchoff.
so does the syntax allow something like
PROGRAM BYE
FOR i:=0 TO 9
SAVE(GRi to Savedi)
Or do i need to reference each variable:
For i:=0 to 9
If i==1 Save(Gri to saved1, saved(1) eor whatever)

Similarly for lists

Of course, one can reference a single list element, but that can only be something simple such as an integer, rather than a list, string or grob
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I know (i think) some BASICs will treat GR+I or gr+str(i) like another variable.
which is a lot easier than manually creating 25-30 grob variables, should you want
to animate 1s-worth of video.
to◄►

A language such as C, one could simply declare an array of type grob/list/string, having defined how that is stored. Having the ability to do this makes iteration more practicable, but is not always available.If it can be done on the HP Prime, what is the relevant syntax?

That's an excellent question, and I'm afraid I don't know the answer. I'll explore on my own Prime, but hopefully someone like Tim or Han who knows more about the Prime will respond sooner.