The which is simply an alternate construction of the relative pronoun which (probably only introducing nonrestrictive relative clauses).
the which: (archaic) a longer form of which, often used as a sentence connector
Source: http://www.collinsdictionary.com/dictionary/english/the-which
The construction has fallen out of habit -- Harper Collins marks it "(archaic)" -- and it appears now only in old writing, or in new writing that's trying to sound old. The reason why the in the which fell out of favor is probably because the there adds nothing to the sentence but a certain fustian elegance. Non-restrictive relative clauses are already presupposed, hence definite; nothing is served by adding a definite article.
As noted in the question, Latin qui, quae, quod, quis, quid, and all their descendants still spelled with qu in Romance languages are historically cognate with what, why, which, etc. via Grimm's Law. Where Romance languages have qu-words in their grammars, English has wh-words.
More interestingly, also via Grimm's Law, where Latin had demonstrative t-words like tantum and talis matching interrogative qu-words like like quantum and qualis, English has demonstrative th-words like that, then, there, thither, thence matching interrogative what, when, where, whither, whence. Just as PIE labiovelar *kʷ became labiovelar stop qu- (originally pronounced [kʷ]) in Latin (and most other IE languages) and labiovelar fricative wh- originally pronounced [xʷ]) in English (and other Germanic languages), PIE dental *t became dental stop t- in Latin and dental fricative th- in English. Those are two of the 12 systematic consonant changes that make up Grimm's Law.
