Well i only had the problem with "Could not download Android Core.zip" and after failing with cygwin and therefor not being able to compile the source i continued reading the source to find that all the program is trying to do is:
1) download core.zip from the server (and this is where it failed causing the error, and im still pretty sure it has to do with the URL in the source code)
2)rename core.zip to "processing-android-core-" + Base.VERSION_NAME + ".zip" which is "processing-android-core-0184.zip" is our case
3) save "processing-android-core-0184.zip" in the sketchbook folder so that processing didn't need to download it again
So what i did was just to pull core.zip of the server manually, rename it and the place it in the sketchbook folder.
thus solving the problem and everything is now working as (i think) it should for me.
So im not having your new error and i have no idea what's causing it, sorry
EDIT: ok i've done some reading and it appears that your error comes from this file:
http://code.google.com/p/processing/source/browse/trunk/processing/android/tool/...As you can see the error is showed when processing fails to verify that the AVD (androice virtual devide) exist or fails to create the AVD (or both):
Code:(ECLAIR.exists(sdk) || ECLAIR.create(sdk))
From what i could tell from your post there is no stack trace meaning a excetion is not thrown, which might mean... something :/
but if i had to guess i'd say that you haven't installed the Android SDK correctly so try reinstalling it