There's no general answer. I've met many fundies who have read their book and are familiar with it. I've also seen many who (though I cannot be certain) seem to have read maybe a handful of the most popular verses, if you're lucky one of the Gospels, and just parrot the usual talking points.
Cherry picking, of course, but that's kind of necessary. You can't not cherry pick from a self-contradicting book.
As for the Paulians vs. Christians thing... well, they do ignore a lot of what Jesus said, but they also ignore a lot of what Paul said. Take the whole "Marriage is the basis of society" crowd, for example, completely ignoring that Paul said that people should ideally be celibate for life and marriage is only a last resort for those that cannot control their urges (1 Corinthians 7). Bottom line, people ignore the parts of the Bible that are inconvenient, regardless of who said them. It just happens that a fair bit of Jesus's stuff is inconvenient, and a fair bit of Paul's stuff is not.