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Hi Kristen -
You can do both. You used the word "publishing", which to me means Tableau Server. Via the security permissions of Tableau Server, you can choose to disable your viewer's ability to download the published workbook and also you can turn off the "view data" function.
Your second question will involve a quick calculated expression. Let's say your survey question (?) has some sort of ID associated with it -- you'll want to count the number of times we see that ID like this:
You also don't want to show the particular question unless you have three responses, so:
Count([ID Field]) > 3
The expression above will return "true" or "false" on a per-question basis. You'll use this new field that you create as a filter in your report, choosing to only show "true" values. Hope that makes sense