 Re: conjunction
a) As still is an adverb it can't join clauses into a single sentence - only conjunctions can do that.
b) As before, your sentences are invented, uncontextualised and rather unnatural, so it's almost impossible to say what would be used. Most of them seem to be contrast rather than concession to me.
c) As I said before, still is more common in spoken English, where ideas are usually either co-ordinated or just juxtaposed. Here are some authentic examples of its use. + means there's a pause:
I'm sure there's some awful battle where we got er knocked about + but still I hope that's not a presage of what's gonna happen now
I'm getting old + yeah that's older + still yeah it's funny + you don't feel any older inside
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