I think that your model #2 is fine, however you can take a look at the more complex model which stores questions and pre-made answers (offered answers) and allows them to be re-used in different surveys.
- One survey can have many questions; one question can be (re)used in many surveys.
- One (pre-made) answer can be offered for many questions. One question can have many answers offered. A question can have different answers offered in different surveys. An answer can be offered to different questions in different surveys. There is a default "Other" answer, if a person chooses other, her answer is recorded into Answer.OtherText.
- One person can participate in many surveys, one person can answer specific question in a survey only once.