Export / import content via MySQL
Is there way via phpMyAdmin or importing SQL into the database? Yes. Between 2 Drupal installs of the same version that is possible, but that comes with a big caveat. You need to know exactly what you're wanting to import and that you're not missing anything. 

For example, say you want to import roles. You could export/import the role.sql from the role table, but that would only get you the role definition. If you want the permissions with those roles, you'd need to copy over the role_permission table. Depending on your needs this might work; the smaller number of table dependencies, the easier this approach can work without a problem.

However, in your case, you've mentioned a few Drupal components that span multiple data tables (e.g. node types, views, fields, etc.), not to mention other configurations (e.g. module settings in the variable table) that a module might depend on to behave the same between 2 installs. To take the example above, the role_permission is filled with permission items that are created by various modules. There might be a problem if you don't have all the same modules installed on your new site.

In these cases, and in general, you're better sticking with the tools that the community has created to handle importing the various components of Drupal. For example, the maintainers of Views have already built in a export/import feature for views. There many posts on Drupal Answers discuss these tools (and how to use them). Here are a few examples:


Features (content types)
Feeds (content/users/taxonomy)
Drupal-to-Drupal migration (users/profiles/taxonomy/content)
User Import (users)