Q1: Technically, as is the preposition which introduces the back half of a comparative construction, with the front half suppressed because it's basically irrelevant.† In this instance you might think of it as a such ... as ... construction:
... in such a way as I have never been able to confide in anyone [in that way] before ...
In effect, it's a way of adding a second, parenthetical clause to the sentence:
I hope I shall be able to confide in you completely
(I have never been able to confide in anyone in that way before)
and I hope that you will be a great support and comfort to me.
Q2: In the 18th and 19th centuries (and among schoolteachers well into the 20th century) the prestige dialects of England and employed shall for will in the first person. Probably you can safely ignore this, unless English examiners in your country are at least fifty years out of date.
† I must tell you that the Cambridge Grammar says this is the front half of the construction; but I find their explanation of this impenetrable.