In 'that there is that which transcends....' the first "that" is a subordinating conjunction; it introduces the clause that tells us 'what the interior of our language informs ["us"? - is there a typo here?] of'; the second "that" is a demonstrative pronoun; it stands for 'something indefinable'.
As for 2, this sort of thing either says something very important but very hard to grasp, or something approaching the entirely vacuous and self-evident. I'd guess that what is in the writer's mind is something like this:
Becoming really at home with a language involves much more than just knowing the words and the grammar. The details of how language works tell us that there is much more to it than just 'the details of how it works'.
But I'm open to correction.
Student or Learner