Will my husband have any problem getting visa/green card?

Two issues in your case are namely that your spouse entered US without inspection and so, this may hinder his ability to adjust status, especially if your visa was filed after the s.245(i)INA sunset date. Of greater concern is the fact that because your husband reentered United States twice illegally after his deportation in 1995, he may be subject to s.241(a)(5) INA Reinstatement. because, he was deported in 1995 and he returned twice [1995 and 2001] both reentries occurring before and after the Apr. 1, 1997 effective date of s.241(a)(5) INA. You should not file anything with CIS until after you have consulted with an experience immigration attorney.

It's unclear if he was expeditedly removed in 1995.?In any event it appears he needs waiver of unlawful presence(I-601 waiver). He can file the waiver in march while waiting in the US. If approved he can then return to his home country to apply for immigrant visa. Your case is not simple so you will be better served by having an immigration lawyer on your side.

Apparently yes. However, we need to confirm if he was ever ordered deported and whether he has to apply from outside of the country.

He is not eligible to legalize his status within the US since he entered the US unlawfully. He would have to consular process in his home country and he would be subject to the 10 year bar to reentry because of the overstay. The bar to reentry can only be waived by a showing of extreme hardship to a US citizen spouse, which is fairly difficult to prove in most cases.

All Immigration questions are very fact intensive, and no easy answer can be given to your question without meeting with you in person and delving into your life history and what you might be eligible to apply for from USCIS.

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case, advise you of your options and, if possible, make sure that the necessary paperwork and documentation is presented so as not to delay the process.