1) What is the proper syntax to declare a recursive regular expression using (??{ code })

I'd say, the only proper way is to not use it. (??{ }) (and (?{ })) have many problems. Scoping is one of them. (??{ }) is inefficient, not self contained, and in general, a PITA to use. On top of that, they're buggy. And may crash your program:

$ perl -wE '/(??{ s!!! })/'
Use of uninitialized value $_ in substitution (s///) at (re_eval 1) li
+ne 1.
... repeated many times ...
Segmentation fault
$
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The reason the constructs are still marked experimental is that noone has stepped up and said "Not only do I know how to fix the issues, but here's a patch". For all we know, noone knows how to fix the issues.

Does anyone know what version of perl the following started throwing a strictures error our $x = qr/(??{ $x }/ and of course why.

Somewhere between 5.8.1 and 5.8.8. And probably due to a bug fix.

Can anyone think of a single instance where (??{ code }) would be used for recursive regular expressions over the (?PARNO) feature, or should that usage be deprecated from one's toolbox?

Only if code returns something different - perhaps because parameters are passed. Other than contrived examples, I cannot come up with something where I'd prefer to use such pattern.