All 3 Uses

however
in
The Overcoat, by Gogol
(Edited)

However much the directors and chiefs of all kinds were changed, he was always to be seen in the same place, the same attitude, the same occupation; so that it was afterwards affirmed that he had been born in undress uniform with a bald head.
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however = regardless of how
This, however, inspired him with such terror that he ran off with all his might, and therefore did not scan the dead man closely, but only saw how the latter threatened him from afar with his finger.†
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however = a word used to connect contrasting ideas as when using though, in spite of that, in contrast, nevertheless, etc.
Occasionally, however, he was interrupted by gusts of wind, which, coming suddenly, God knows whence or why, cut his face, drove masses of snow into it, filled out his cloak-collar like a sail, or suddenly blew it over his head with supernatural force, and thus caused him constant trouble to disentangle himself.†

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?"