Check out the Customizing Labels, Messages, and URLs article. To customise the label I think you’ll need to use a language file.

If you also want to change the slug in the URL, try adding this to your bp-custom.php file define( 'BP_MESSAGES_SLUG', 'mails' );

Have you tried using bp_core_remove_nav_item( 'slug' )? There is also a function available in BP to remove sub-nav items bp_core_remove_subnav_item( 'slug', 'subnav-slug' )

Then once you have that information you could do a simple check when filtering the text.

e.g


if ( is male ) {
// this must be a male so filter the text to say 'his'
} else {
// this must be a woman so filter the text to say…[Read more]

No, it wouldn’t change. You would need to filter the text accordingly depending on the gender they specify in their gender profile field.