If you qualify, H and L visas are certainly more secure than an F visa.
The law is uncertain. This type of entry will be left at the discretion of CBP. I have a blog entry on this subject. Please review it: http://forums.immigration.com/blog.php?u=1
This is a touchy topic. As long as you revealed to the Post during your last entry that you were married, I see no problem with the 130/485 combo.
You can apply for her and he can be a joint sponsor on the affidavit of support. No problem.
I can think of only a tourist visa or ER. But once your husband becomes a US citizen, he can get her green card.
1. From what you have described, I see no reason why you cannot file for their I-485 and have them stay.
2. He can legally stay in USA as long as USCIS receives the extension request (Form I-539)before the expiration of his current status. He can stay till the request is decided or till the time for which the extension has been requested, whichever comes first. It can take several months for the application to be decided.
Just contact the US consulate closest to where you live to find out the formalities and fees. Basically, you need to file a visa application and interview with the consulate. They will tell you what to bring with you.
All he can do is try. There is no way to be certain, but being abroad already should help a bit.