Some of this can be answered definitively, some is very grey and “it depends”.
Plugin Installation and Storage
Plugins are stored on the server in the filesystem. The plugins may rely on data that they store in the database. As a general guideline (ie for typical plugins – there will be exceptions) – you can upgrade and downgrade plugins by modifying whats on disk and the settings should carry over.
Plugins are normally stored in wordpressrootdirectory/wp-content/plugins and a few will be stored in wordpressrootdirectory/wp-content/mu-plugins – If you remove plugins from these directories they will stop working, and if you place new uncompressed plugins in these directory they will be able to be activated.
Database Restoration
In the general case you will need to restore the entire database as its generally impractical to find, track and apply only updates to the database.
I say “in the general case” because if you are using a more complex database setup this can definitely be done, but this is down well outside the typical general webhost considerations and relies on previously configured database setup. The reality of it is if you could do this kind of thing you wouldn’t need to – you would be using a database with replication and simply switching the replica. This is in the realm of if you need to ask on WordPress development you don’t have the knowledge. Its a custom skill outside of WordPress.
A 10GB database would seem pretty massive for WordPress. Are you sure this is the size of the database and not the size of everything including images/video stored on disk ? If it truely is the size of the database you really should be wondering if shared hosting is a practical option – you would be in the top 1% of WordPress demands – possibly in the top 1% of the top 1%!
If the 10GB includes images and video on disk it is possible to speed up the migration if you have access to the disk (for example by presync’ing the data, migrating, then syncing disk updates).
Plugin Data Retention
No, plugin data should not be lost. You may need to do a global search and replace to access the data on an alternative URL, and hooks to third party sites may stop working until the settings are updated, but this is generally a minor concern.
Reinstallation of Plugins
For almost all plugins, plugin data other then media is stored in the database. Media is stored on disk with links in the database. If plugin data is lost you won’t need to reinstall the plugins (assuming they exist on disk) but you may need to reactivate the plugins. That said, this question does not make sense.
Insights and best practices for a smooth transition
You asked, so I’m answering. Assuming you have not misrepresented the size of the database (and I suspect you have), there is no way you should be using shared hosting for a 10 gig database – especially with Godaddy team. If your database really is 10 gigs, you either need to clean it up so its a tiny fraction of that, rebuild your application so its smaller or use dedicated hosting. 10gigs of database requires a significant amount of memory to run properly, and this is well in the realm of a dedicated server.
You also want a dedicated server so you can have a proper systems administrator handle the site using tools not available in WordPress or on shared hosting. Things like database replication, filesystem level snapshots, diagnosing resource bottlenecks and a raft of other thing.