Is it permissible to adopt one of two opinions from two different schools of thought regarding two separate issues mentioned in a single hadith, or is it obligatory to adopt one of the two schools of thought for both issues?

The hadith to which the questioner refers is not known. The Shafi'is have two opinions regarding the nullification of wudu' by touching a woman: one is that it does not nullify wudu', and this was authenticated by Al-Ruyani and Al-Shashi; the other is that it does nullify wudu', and this was authenticated by the majority. As for the Hanafis, they hold that touching a woman's skin does not nullify wudu' at all, and this is the fatwa given. An ordinary person may move between madhhabs or imitate a scholar on a particular issue, provided that it is not merely out of caprice.