Your questions (and then some) about JHU are answered in this thread: http://talk.collegeconfidential.com/johns-hopkins-university/1880071-hopkins-vs-brown.html#latest
Post if you have additional questions about JHU or its Neuro program (which has a cognitive concentration). Additionally, yes, you could major in Psychology or in Cognitive Science (which also has a Linguistics minor). Heads up, the Neuro program is more interested in structure/anatomy and on a molecular level as opposed to the cognitive approach, though the cognitive concentration does give you some of that. I bring up Neuro just because it is more popular than these other related majors at JHU (not that that necessarily indicates anything).