Will be there any challenge in Immigrant Visa F2A or Non-Immigrant K3 Visa approval.

[Lobster]

I am a US PR. I will qualify to apply for US Naturalization in November 2016.

I got married back in Nov 2015. My Spouse is outside USA. I applied I-130 F2A, in Nov 2016 @ CSC. Since then I-130 is pending with status "Case transferred to Local Office". I called USCIS, and was told that i'll be interviewed for Initial I-130 Interview. Because i received my PR, through my ex wife, (Good Faith Waiver), back in 2012.

Well, After my second marriage, My current wife applied for a F1 visa for her Masters degree in Feb 2016, She stated on her F2 Visa applicant about our marriage and was asked @ the interview about me and was rejected,stating that she should wait for her immigration Visa. Before this rejection and our marriage, my wife was also rejected for 2 visit visas' but that was way before we got married. I was not aware of those rejections.

Ques:
1) Let's say I-130 gets approved, Will be there any challenges like (Rejection) @ the embassy cause of her previous Non-Immig Visa rejection, or my previous marriage ?
2) By the time i get my Citizenship by Feb 2017 and I-130 is still pending. Can i apply for K3 visa, pending I-130. also any, same challenges reason as in Ques 1?

[daggit]

Which country is your current spouse in at the moment?

Her multiple past visa attempts could come across as desperation to get to the US. In addition, your marriage-based GC, followed by petitioning a second overseas spouse are likely to draw scrutiny. Your best bet would be to provide as much evidence of a bonafide marriage.