1) From the conversations I've had, all sorts of people go. I know a guy who was top of his 1L class, decided to go study in England for the summer instead of taking a job. When he comes back, he still has OCIs lined up, and he'll still be the #1 ranked guy. Plus, many overseas study programs have internship elements, so you can still get some "work" in. I'm planning on going to Scotland for 3 weeks, and then 3 weeks in London next summer. With sports in college I never had a chance to go abroad.
2) Anything positive that makes you stand out from the pack is always good from a job perspective.
3) Doing things that you are interested in doing will make you happier in the long run than trying to fit into the mold of what you think a law student should do.