Hi @Emily_Baadsvik, welcome to the forum! 
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Congrats on the new job! 
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I am also curious to know, is your company an end user of this Retool application, or do you have edit access? This will be crucial in order to be able to write new queries and create new components on the app, to do all of the things you mentioned.
For example, to solve a, we can use the "Toolbar Buttons" as @matth mentioned, or we can create a Resource query and query the database using SQL:
SELECT * FROM table_name WHERE profile_status != 'Complete'
We can then connect the output of that query to your current table or a new one, and display only the filtered rows.
Similarly, we can create new queries and table components to solve 'b' and 'c.'
Here is a SQL Cheatsheet that can help getting you started.
If you don't have edit access, you may want to contact the admin of the Retool app you are working with.
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