I tend to think "whatever works best for me" nowadays.
On the thumb round the neck, I tend to use both ways now, but I learnt originally to play with the thumb - actually to use it for fretting the 6th string if necessary (I believe that's my folkie past coming through...)
On the shaking the neck when playing vibrato, I noticed a few months back that SRV did it when I was watching a DVD. Hoho!! I thought, this is how he got that enormous, sexy, and accurate vibrato on two-fret-bend notes... that's for me, I thought... But can I do it? Can I f... (old horse, new trick, etc :( )
As for holding the pick - I use several different methods (including not holding one at all), they all work in different ways and produce different sounds.
And finally (why can I never write short, punchy posts like most of you?) on those days when the guitar just isn't working properly - it isn't you btw! :) - don't be a slave to it, you have two options: put it down and do something else, or keep playing and make the wretched thing do what you want... I just pick the option that seems most enjoyable at the time.
Does anyone else notice that, invariably, a bad guitar day is usually followed by a day when your playing is, er, "godly"? But unfortunately no-one else is there to hear it! (Philly, I think I know what your answer might be, but I'm not sure I believe you :lol: )