I would like to know what kind of phrase/clause "as far as I know" is, and why.
This is an adverbial clause, which is also a dependent or subordinate clause.
In 'Non-assertive Epistemic Adverbs and Deontic Necessity' at http://semanticsarchive.net/Archive/jE2MDk3O/ESSLLI03_paper.pdf Demet Corcue writes:
Epistemic modal adverbs such as perhaps, maybe, certainly, sure, surely etc. are analyzed under the label of discourse markers.
His definition of discourse markers would certainly include the clause as far as I know.
I am one of those who thinks that the traditional label 'sentence adverbial' is a misnomer, and would class both perhaps and as far as I know as (single- or multi-word) pragmatic markers subclass modality.
Pragmatic markers fall outside the 'central identity' of the matrix sentence:
syntactically: they are parenthetical (a grammatical sentence will be left if they are omitted)
semantically: they do not form a direct part of the statement in the matrix sentence.
They are used to facilitate conversation, structure discourse, or, as here, to add a comment to the base sentence. 'As far as I know' adds a comment relating to the reliability ('truth value') of the statement in the sentence proper, and hence is a modal pragmatic marker.