Top bar and login access

After the update, has appeared an access bar at the top of the page (see screenshot)

Did you recently update JomSocial? That bar is a community toolbar put there by JomSocial, not JFBConnect. If you're looking to remove it (or portions of it), you will need to contact the JomSocial team, or look through their settings/code on your site.

The home page by default (in Spanish) appears correctly (except the top bar above) but if you click on the English language, instead of going to the same page as in Spanish but in English, It goes to a login page (see screenshot).

This does not seem related to JFBConnect. Please check the menu item that you have created for the Home menu item for the English language. If it is set to Registered, then Joomla will force you to go to the user login view. If it is public, please check any SEO extensions that you have installed like SH404SEF and make sure that the English URL is not being redirected to the en/component/users/?view=login URL.

I hope this helps narrow down the two issues, but let me know if you think there's a problem caused by JFBConnect.
-Melissa