are you talking about the inbox of your mail client (e. g. outlook)? This is something that should be customized directly inside your mail client not within SharePoint or Nintex.
For outlook you can have a look here: Automatically change incoming message colors and fonts based on sender, subject, or recipients - Off...
For other mail clients you should have a look at the respective documentation.
So you mean the "My Workflow Tasks" webpart?
Easiest way to customize this webpart is to place another CEWP or Script-Webpart on your side and use JS/Jquery/CSS to style the content of your webpart. If you need to perform this on mutliple sides, a delegate control injecting js/css would be a possibility.
Unfortunately there are no such designing options out of the box.
You can create another Workflow on your Task-List that should be executed when a new item is added. Use this workflow for checking the properties of the task and set flags (properties/columns) as you need it.
I will try to explain a bit more what I was thinking of:
If you want to check your tasks regularly (like daily) and not only once when the task is added, you can create a site workflow instead of a list workflow and schedule that site workflow to run every day for all tasks of your task list (or every hour if its necessary).
However, I'm quite sure you can't display this custom picture inside the "My Workflow Tasks" webpart by default. You may need to create your own by using e. g. a content search webpart. Or simply use a list view from your tasks list. You can configure a list view to show only items for the current user by using a filter on a column and the value "[Me]" to check for the currently logged in user.
Let us know if you need further help!
Unfortunately I can't have enough resource for running search service, So currently I can't use content search webpart.
Do you know any way that I make another "my workflow tasks" for specific workflows ?
You are using your SharePoint without a search service? Are you using any other search experience? How are your users supposed to find documents/data in SharePoint?
If you can't use content search webpart you can try to use the list webpart. As workflows normally only write tasks to one specific task list, this should be enough for you. Open your page in edit mode, add a webpart and chose your workflow tasks lists listview webpart. Afterwards you can change the view to show whatever columns you want to.
Another way would be to create your own custom webpart via visual studio as this gives you full flexibility on creating your webpart but of course requires more effort and knowledge.