All 3 Uses

however
in
New Moon
(Edited)

The proof, however remote, that—somewhere in the same world where I lived—he did exist.
Chpt 10

however = regardless of how
I would appreciate it very much, however, if you would send my thanks to your masters.†
Chpt 20 *

however = a word used to connect contrasting ideas as when using though, in spite of that, in contrast, nevertheless, etc.
As I stared at his too beautiful face, trying to understand the change, it suddenly struck me that I was really here, in Edward's arms, however fleetingly, and that we were not—at this exact moment—about to be killed.
Chpt 22 *

however = regardless of how

Definitions:

(1) (however as in: However, complications may...)
though (or another expression that connects contrasting ideas)

Based on idea 1 we might not expect idea 2, but this is a way of saying that even though idea 1 exists, we still have idea 2. Synonyms include in spite of that, despite that, nevertheless, nonetheless, on the other hand, in contrast and but.
(2) (however as in: However much she tried...)
to whatever degree (regardless of how much; or whatever unspecified amount)
(3) (however as in: However you do it, get it done!)
in whatever way
(4) (meaning too rare to warrant focus)
Much more rarely (and arguably incorrectly), however can be used to intensify the word how, as when one says "However did you find her?" Grammarians would suggest using two words for that usage: "How ever did you find her?"