SQL design for survey with answers of different data types

Question

I am working on an online survey. Most questions have a scale of 1-5 for an answer. If we need to add a question to the survey, I use a simple web form, which does an INSERT

Answer 1

that I'm posing is "I'd like to store data of an arbitrary type without doing any coding..." Is this hopeless?

Yes, it pretty much is. There is no "good" solution to the problem you're posing. The "best" is as Dave Swersky and Larry Lustig described it:

A Question table, which stores the question, possible answers (if it's multiple choice) and a question type

An Answer table, which stores the answer to a question (FK to Question table), serialized as text. Varchar(4000) or TEXT datatype, preferably the former unless absolutely necessary.

It's up to your application logic to determine what the value means based on the type specified for the question.