Sounds like your being too casual with your green card status but you have to weigh your risk tolerance. Personally I would focus on citizenship and then you can come and go as you please.
You have to be patient. If uscis needs anything they will issue rfe. I know it's nerve wrecking but this is the process. Try to schedule more in person meetings if possible.
No experience with embassy stage, but the i134 was not asked for, although I sent it to my then fiancée in advance. If you make it past the embassy then you will definitely need it for I-864.
The issue is the visa was granted under the incorrect pretense and perhaps the parties may be getting charges of misrepresentation. The parties should have just used the spouse visa process.
Actually both couples must be unmarried at the time the petition is filed and remain unmarried until the US entry. The visa should have not been granted.
How many times have you met in person? What was the purpose of the visit? If the intent was to marry and adjust status before US entry, it's considered fraud.
Hopefully you filed for the employment authorization card and requested SS card. With that you can apply for dl or state ID. Until then you would have to use foreign passport.