1. Not an issue, unless your wife visits North Korea, Iran, or Syria. Also, if she stays more than 6 months or gets in trouble with the law in any country other than her current one, she would likely need another police certificate. In any case, make sure your wife updates her travel info on the DS-260 form prior to her visa interview.
2. Not an issue for the consulate in Seoul if you have sufficient liquid assets, preferably in US-based accounts. IIRC, @Redro has first-hand experience with this.