Is there a module to translate blocks and pages with language modules?
Block languages submodule of i18n
Submodule i18n_block, included in the i18n module, could be what you're looking for ... or at least address part of your question.
Some more details about it:

This module provides support for multilingual blocks.
You can set up a language for a block or define it as translatable:

Blocks with a language will be displayed only in pages with that language.
Translatable blocks can be translated using the localization interface.


Bean module
Consider looking at the BEAN module also. It offers all sorts of enhancements as compared to the (old fashioned) blocks. And possibly you may want to combine it with modules such as Entity Translation to achieve your goal.
The video tutorial Drupal Bean module tutorial - using Bean Admin UI provides a great introduction to really understand the power of the BEAN module, and the kind of things you can do with it (by only using site building techniques, no custom coding involved). It also shows how the Bean module transforms Drupal blocks into fieldable entities.
Managing translations
To actually &quot;manage translations&quot;, there are a few typical modules like these (quotes from their project pages, with some bold markup added here):

Translation Management Tool (RC-version for D7).


... provides a tool set for translating content from different sources. The translation can be done by people or translation services of all kinds. It builds on and uses existing language tools and data structures in Drupal and can be used in automated workflow scenarios.
This module does not make i18n or any other language module for Drupal obsolete. It does only facilitate the translation process.

This module seems already well ported to Drupal 8 also, so much that it is already recommended as a successor of the Translation Overview module (which is about translations of  nodes), which also refers to the Translation Table module (which is about translations of taxonomy terms and menu items).

Translation Management  (No version for D7, only for D6).


... provides complete workflow management for multilingual Drupal sites.
Content managers can manage all translations from one central page. The module shows which contents need translation and notifies translators about what they need to do.
... The module introduces a new Translator role. This role allows translating between specific language pairs. Translators have individual job queues, showing documents that were sent to them for translation.
... Translators can translate everything without having to learn Drupal administration. Node contents, menus, taxonomy, CCK, blocks and strings are all translated from the same interface.

Note: even though there is no D7 version (yet), there are quite a few D7 related issues (and there is a GIT branch for D7 also). And there is the Drupal-Translation.com website with tons of interesting documentation.
Interface translations
The translation of the interface is about the translation of various text strings used throughout the site, like labels used on buttons such as submit, or on tabs such as view or edit. They are the same on all sites (no matter what actual content is contained in a site).
To manage these kinds of translations, there is the Localization update module.
More translation modules
Translations in Drupal is fun, here are a few more to finish:

Language Icons.
Variable.
Title.
Entity.