I want to deliver to my customers a unique code, which they will enter when starting a survey. I then need to parse this code (looking up in a database) which will then direct them to appropriate questions in the survey. Example: if they enter code 001002, the first half will tell me the store they visited (001), the second half (002) will tell me when they visited. I then want to display on the second screen "Thank you for visiting our New York store" (as dictated by the 001.

Do I need to introduce a custom question type (and where is documentation for this), or is there some "hook" I can use to do these lookups?

I should not require them to sign in, the code they enter will be sufficient, so it should be an anonymous survey.

You should be able to do this with a simple short-text question and Expression Manager/relevance.

In your relevance equations, you can use the string functions to handle the entered code.