You can use the collect ideas feature of PollUnit. Your students can add ideas (or questions). Those questions can be upvoted. You have different sorting options including vote count. Optionally you can allow commenting per question.
You can also create PollUnit votings where participants can also add options or questions. You can choose from different ...
With PollUnit you can create idea collections and polls. A idea collection can be converted into a poll or you allow participants to add options directly to the poll.
A poll/voting can be cloned. If necessary, options can be removed/added and participants can vote again.
PollUnit does not offer a flip of coin in case of a tie. However, when closing a poll, ...
Survey monkey is really easy and you can set more advanced metrics. I have used it in market research and it has everything you need and you can even do A/B testing for different questions. Good luck!!
I did a search for "polls" and found these.
Rather than a specific site, I recommend using a Wiki where everyone can add, change, and share the site equally in a public or private environment. Little effort is necessary to set things up just the way you want them.
Have a look at pbworks.com