free websites usually have no or very poor search engine ranking.
the only ones that are free and can promise good visibility on search engines are
www.blogger.com( can integrate Adsense)
www.WordPress.com(cannot integrate Adsense)
these are actually blogging platforms with limited features and flexibility and a limited space that will affect the speed of loading of the website. the kind of website that you want will not be possible with this as videos require a large space(memory).
another thing: if you're expecting people to upload to answer themselves through videos, you have to know that many people are shy or prefer privacy to post a video of them on a public forum.
I'd advice you to start a blog about a happening topic( love, travel, fitness, gadgets, movie reviews, song lyrics, television shows).
you can search for free through Google Adwords keyword tool. it will show the monthly search for a particular keyword or topic.
https://adwords.google.com/o/Targeting/Explorer?__c=1000000000&__u=1000000000&ideaRequestType=KEYWORD_IDEAS
if you're not that good at writing, you can find freelance writers with experience in SEO writing on www.elance.com to write blog posts(articles) for you.