As for the alternate picking, start very slowly and practice your scales by picking in an up/down fashion. You might find that you are picking the first notes on a new string in an up fashion but it will feel normal eventually. Check out http://www.stevemorse.com under his lessons tab. He is probably one of the best alternate pickers I know.
As for chords, get a chord book. Simple.
The rest will fall into place in due time.

But don't ever forget the most important thing. Use a metronome. Noone wants to play with someone who can't keep in time, not to mention it will take you a lot longer to progress without one. You can always download one from the internet, or buy one from your local music store.

As for that idiot you got for a teacher, tell him you want a refund. There is no excuse for not teaching the basics like that. Jerks like that piss me off.

Have fun