May my US permanent resident husband file for an I-130 (Alien Relative) petition for me while I have the J-1 Foreign Residency R

Your U.S. resident spouse can proceed to file the FORM I-130 on your behalf. However, you will not be able to file the FORM I-485 until the visa is available and you obtain a waiver of the foreign residency requirement.

1. Even when there will be an immigrant visa number available for you under the F-2A category, as the spouse of a green card holder after approx. a year and a half from the time your spouse will have filed an I-130 petition on your behalf, you will not be eligible to "adjust status" in the USA unless first obtain a "Waiver" of the 2 year HRR to which you are subject. 2. Yes, LPR husband can file the I-130 while still subject to the 2 year HRR rule.

Yes he can file the I-130 but after that you will not be able to get a nonimmigrant visa at a US consulate so factor that in. By nonimmigrant I mean F-1 or J-1, or visitor's.