Which VCF field do I use to specify a group in Android? And how do I get the picture via URL? I'm creating a VCF file on my website.

1) It works nicely with the export, and most data are being imported, but the group is not created or used on Android.
I've tried using CATEGORIES and ORG
I also tried to look at KIND and MEMBER, but couldn't figure out how to use those, seems to refer to URI's and not a group name in the phone book.
If I export a contact, it doesn't fill in the group in the contact.

2) As I have limited text possibilities (I am going to encode it in QR code), I would like to get the contacts image exported as an URL, but it seems that it completely ignores the URL. I can of course encode it in base64, but then the text is going to be too big for QR code.
Here's a list of valid VCard fields separated into supported/unsupported by Android's vcard importer:  

VCardConstants.java

It currently (4.3) says, ORG is supported while CATEGORIES is not. Check it yourself for more clarification.
You may also want to compare what has changed in 4.0/4.1/4.2/4.3 here.