I don't think either of these statements is true.

This is not a flaw. It is a feature. Arguing about how it should have been done X way is pointless.

I disagree. This is not about subjective aesthetics. There are some fruits that are poisonous and are thus objectively bad, totally apart from the question of what fruit you think tastes best. Some of perl's language design features are objectively bad. For example, the way references are implemented makes it absurdly difficult to reason about simple things like nested sequences. If that complexity was needed to get some positive benefit like outstanding performance, then maybe it would be justified. But there are no significant benefits. They are the way they are because Larry Wall didn't understand anything about programming languages when he made perl.

As for parsing, it is impossible to parse Perl, as it is Turing-complete and nobody has solved the halting problem (yet).

With respect, every language I'm familiar with can be easily parsed except for perl. This has nothing to do with Turing Completeness or the Halting Problem. This has to do with having a sufficiently well designed syntax that tools can easily parse files written in the language without having to implement the whole damn language. That's an important property to have every language besides perl nails it because it is easy to do, but perl doesn't because Larry Wall didn't know anything about programming language design when he started.