Problem with configuration of default front page url in site configuration area

There is something strange when enabling Translation module with Trailing Slash module enabled. On site configuration page there are some mismatches:

Default front page, 403/404 error page settings looks like this:
http://site.com/admin/config/system/site-information/ [input]

instead of usual
http://site.com/ [input]

after disabling Trailing slash:
http://site.com/en [input]

All works fine before enabling Translation module. After installing it I don't get some errors but lost $front_page variable in my templates.

And maybee it is Translation module's issue.