1. For what other pairings of data types does eq ignore type?

   Basically every type. It forces each argument to a string before making a comparison.

2. Is there a way to override this so that things belonging to different data types are always not equal?

   I'd probably write a custom comparison sub to do it.

   use Scalar::Util qw( blessed reftype );
   
   sub comparifier {
       blessed $_[0] eq blessed $_[1]
    && reftype $_[0] eq reftype $_[1]
    &&         $_[0] eq         $_[1]
   }
   [download]

   Along the same lines, you might be interested in Reference assessment techniques and how they fail, whose subtext is "gosh, it's hard to figure out what a scalar really is."

3. ...how can I detect overloaded operators?

   Overloading applies to objects, not operators. (In Perl 6 you can override operators and/or write your own.) If you want to know if an object is overloading, use overload::Overloaded( $obj ). If you want to know if it's overloading eq in particular, you can check overload::Method( $obj, 'eq' ), but you'll also have to look for stringification (overload::Method( $obj, q{""} )).

4. ...how should I understand it?

   Just that eq forces its operands to be strings in order to do its job. A regular expression stringifies as you've found (it's a blessed reference to an undef with regex magic added).

You might also be interested in overload::StrVal( $obj ), which gives you the string value of $obj without string overloading. For a regular expression, this is similar to "Regexp=SCALAR(0x1d10860)".

I hope this helps.

Updated to fix a thinko in comparifier, thanks to AnomalousMonk.

Updated again thanks to jdporter.