A good way of handling the anonymity is to include a question which requires the respondent fill in a blank or a text box with some phrase, word or number that is unique to them. That way, you can see who answered the survey and identify the samples that have been done by the same person. Since the person taking the survey makes up the word/number/phrase, you don't know who they are. Also, the instructions should clearly state that this word/number/phrase doesn't identify them in any way. No names, address, phone numbers, etc. It should also be something that no one else is likely to use. I might choose, for example, the color of my bike and my shoe size: mustardYellow45
Out of curiosity, I tried looking at two of the survey sites that seem to be among the most popular free ones.
On Mister Poll, I put together
http://www.misterpoll.com/polls/599984 in about 5 minutes. A Survey Monkey version is at
https://www.surveymonkey.com/s/JL9F773 . In both cases, I started the survey with a *required* fill in the blank question where the phrase goes, followed by any number of questions. Both sites allow multiple choice, fill in the blank or other options.
Mister Poll doesn't timestamp the entries, so it's up to you to gather the data every day and figure out who's answered on each day and who hasn't. They allow you to download the answers as an Excel-compatible file which is incredibly handy. I'd suggest that you not list the poll in their directory. That way, no one will find it in a search and only those people you share the link with will know about it. You have to be 13 to create a poll here. Whether you are or not, I'd strongly recommend getting help with your survey from a parent or teacher.
Survey Monkey is free if you live with limitations. A free survey won't allow you to download the results in a spreadsheet, but it does timestamp the results. It will be a more difficult task to go through the responses one at a time, but at least the site keeps track of when the survey was answered. I don't know what the paid options look like since I created a free account and had never used this before.
Again, make sure you run your survey past a parent or teacher before posting it, and don't include any information that would identify you. Explain in the description what the survey is for, how you plan to use the data and that anyone is free to quit answering at any time. If you ask for anything personal, like "where do you live", "how old are you" and stuff like that - that's okay if it can't identify the respondent, but if it's optional, make that clear too.
Please write back if that's not clear or if you have any answered questions.
I'll share the results of the surveys I posted above if anyone cares, but I'll guess that the results will show that everyone agrees on the best science website.
Howard