jquery 1.7 with jquery update kills field managing

Drupal Core is not made to work with jQuery 1.7. I haven't had the exact same issue as you've had but there are other similar issues that will happen:

• General issue: #1386294: Release jQuery 1.7 for Drupal 7
• #1448490: Remove the states.js overwrite as it was fixed upstream
• #1448494: jQuery 1.7: field_ui.js use attr for property

There are things you can do to fix these issues though:
You can create your own module based on jQuery Update to replace states.js by your own with the fixes mentioned above.
You can replace field_ui.js with your fixed one in the template.php of your admin theme with hook_js_alter().

/**
 * Implements hook_js_alter().
 */
function rubik_js_alter(&$js) {
  if (isset($js['modules/field_ui/field_ui.js'])) {
   $js['modules/field_ui/field_ui.js']['data'] = drupal_get_path('theme', 'rubik') . '/js/field_ui.js';
  }
  ...
}

Or you could tell your custom module based on jQuery Update to replace js files to only use jQuery 1.7 on non-admin pages.

There´s a fix for jquery update that´s here.
Could this work?

I have some issues with jQuery, and I "think" that could be because of this, because I´m trying to use twitter´s bootstrap in a Drupal 6 installation.

This is not related to twitter bootstrap directly and issue are allready open on jQuery update. So close it as duplicate.

#1498858: [meta] attr and prop (help is welcome!)
#1448494: jQuery 1.7: field_ui.js use attr for property (you will find a fix on comment #9)