3 blogs on one site with the same header menu?

The first, and likely best, solution is to use a WordPress network where BLOG 1 resides at example.com.

BLOG 2 is a totally separate blog, but within the context of the network and lives at a subdirectory like example.com/blog2. And so on…

The second solution is to use a plugin that pulls in feeds from external blogs and saves them to BLOG 1’s database.

The third solution is to use iframes to include BLOG 2 on a separate page on BLOG 1.