Combining 2 drupal 7 sites - how to move modules?
I don't know for the menus, but for modules that doesn't implement any export functionality (either custom or contrib), take a look into the 'variables' table.

for how unpractical it may sounds, export the table data, keep only the 'module_*' entries of the module you need and insert the in the new site database, after you install the modules. You will have to change the sql from inserts to updates too.

yes, extremely unpractical, but i can't think to an automated routine for it.

also, probably you are forgetting to export users too (and custom roles).