A small patch to add the home variable to i18n variables for Administrator translation

Same here

Perfect, thank you. By the way, you could also put a usual "Implements hook_variable_info()." comment before function custom_breadcrumbs_variable_info. :)

To prove that it works correctly, let me attach some screenshots of my own experiences!
I also hope it helps somebody how to translate the "Home" text in Custom breadcrumbs settings.

BEFORE applying the patch:

AFTER applying the patch:

How-to steps:

1. apply patch (e.g. in NetBeans)
2. go to admin/config/regional/i18n/variable and check "Homepage breadcrumb", then click "Save configuration" like this
3. go to admin/config/user-interface/custom-breadcrumbs, now you can see that "Home breadcrumb text" is already a multilingual variable: http://drupal.org/files/Custom_breadcrumbs_05._admin-config-user-interfa...
4. save the English text:
   
5. click on your other enabled language(s), and save the appropriate text(s):
   

Marking #504400: home reference and i18n as a duplicate of this issue. Also, committed the above patch with the proper documentation header in 8532947.