I have this problem as well. In general I sweat a lot, but I've always had sweaty hands. The problem I ran into was I would trash strings after a single playing session...they would turn black! I stopped playing for years because of this. Now, I'm take care to wipe my strings down thoroughly when I'm done and change them frequently...every 3 to 4 weeks. Strings are cheap these days, so it's not too bad. Even still, my strings start to turn black as soon as I start playing.

Keep a towl handy to dry your hands between songs. I also find that washing my hands thoroughly with hot water before playing helps...not sure why but it does. Also keep a cotton cloth (old tshirt) handy to wipe the guitar neck down frequently.

Powder could just end up creating a cakey mess that builds up in your fretbaord.

I've noticed Anders seems to have this too. Watching some of his lessons, I'll notice sweat marks form on the fretbaord of his guitar. It's nice to know that even great players like him have this problem...and manage to work through it.

As far as keeping a grip on the pick, I've seen where people would score the pick surface with a knife to make the surface grippier. I like the Dunlp Tortex picks. The surface is slightly rough to the touch...just enough to make them grippy. Lots of players use these picks.