アンケートって英語でなんて言うの？

"Please fill in the survey/questionnaire." or "Please take the survey/questionnaire."
"Please," asks them politely to do something.
"Fill in" or "take," asks them to lease complete or answer the questions.
"Survey" and "Questionnaire" are both ways of explaining a set of questions.

The set of questions that the people have to answer is called a questionnaire.
For example: "Could you please fill in the questionnaire."
The process of asking the questions and getting the results is called a survey.
For example:"A recent survey found that 58 percent of people did not know where their heart is."

A questionnaire may be handed out to people after an input session by an instructor, when attending a doctor or the hospital, when giving customer feedback - or in many other possible situations. The 'questionnaire' is the peice of paper the questions are written on - or the list of questions you perhaps see online. A survey and an opinion poll is the process of interviewing or gathering people's reponses so as to use the data to draw conclusions.

A. Why did you go to the business building? I thought you were a language major.
B. I went there to do a study.
A. What kind of study?
B. It was a market research study-- just a few questions and fake scenarios.

When you're doing research and compiling questions; those questions can either be called "survey", "questionnaire" and "research questions".
For example:
-I need people to complete the online survey for my research
-My research questions are aimed at determining the perception people have of our president
-I don't like questionnaires.

Survey is the most common word used when you are conducting a study involving the questioning of people.

If however these are a set of questions you seek to answer through another form of research you might call them investigation questions or inquiry questions.