Aden58

I suppose it depends on how long they've been here if they meet the IRS presence test or not 

If you are a tax person it will be sorted out by the W8-BEN since on it you calculate physical presence as well.. I literally just went through this hahaha

You are the moment not a U.S person for tax reasons. None of them apply. You will have to fill out a W8-BEN form proclaiming this. Once you have your GC you can update the information with your bank.

PEriod of authorized stay.  But sounds like the 3rd option 

You are in a "gray" area. You're not a resident, but you're in a legal status while your I-485 is pending. If you had a B2, or K-1 visa and your I-94 is expired, just carry a copy of the I-485 NOA1 letter on you.
 
Depending on what bank, most I think require a SSN.

Read this guide here
http://www.visajourney.com/content/i130guide2
Good luck!

1. i130
2. G-325a
3. i864
4. i485
5. i765 (optional)
6. i131 (optional)
7. G-1145 (optional)