You can use filters for this. When on board, click "Filters" button, and check member name. You will see number of cards displayed in top right corner, between "Filters" and "Clear all" button.
To see pending tasks, based on your needs you can add "Not market as complete" filter or "Due in the next day/week/month".
If you need this functionality across many boards, not only one board, you can apply filters to the view with many boards. You can learn more about Trello views here.
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