In all probability, yes. The current process requires a showing of lawful entry in order to adjust in the us. Those who can't have to process their cases at the us consulate in their home country. Unfortunately, by leaving the country they trigger an unlawful presence bar thy needs to be waived by showing extreme hardship to a us citizen spouse, for example, before they are permitted to return lawfully.
We're all eagerly awaiting the new regulations that would allow certain individuals t...
You certainly have the right to inform DHS of your suspicions in an affidavit. They might or might not take action, but it is their prerogative. And yes, it's possible for your ex to get conditions removed if he demonstrates that the marriage was entered into in good faith but ended in divorce. The fact that he moved out one week after he got his GC will look very suspicious.
Your question is far too case-specific to be answered on a general forum such as avvo. Hiring an attorney is the best idea. Next to that, much information is provided by the Department of State re: your questions: http://travel.state.gov/visa/immigrants/info/info_3195.html.
If the processing for the provisional waivers is done at the same speed as foreign-filed waivers then it should be about 4 months from filing. This is pure speculation since the program is not in effect.
I suggest you retain my or one my colleagues assistance as it's likely that applicants will have one try through the provisional waiver program and you want to optimize your chances.
If your husband is the petitioner then he will have to submit a complete I-864 and provide all requisite documents as described in the instructions. This is separate and distinct from the form and documents that must also be submitted by the joint sponsor.
There was no law passed today. There was an announcement that the government recognizes the need for comprehensive immigration reform, but the ideas are very vague and general and it's clear that this is the beginning of what will be a long process.