It is good to note that you have great respect for copyright. Copyright has been one of the most abused IP rights, probably because of some inherent weakness in its enforceability. That apart, let me answer your questions one by one.
If I ask the members to write the news in their own words, after reading it in a news website, will that be legal?
Yes, this is the safest method and absolutely legal, and this should be the approach.
If they write in their own words, is it necessary for them to also mention the source of this news, where they read it?
Yes, you will be required to acknowledge, if you are quoting from copyrightable sources or expressing the similar idea in your own words driving inspiration from it.
There is a catch. Some one might argue that copyright subsists only in the expression of the idea, but not the idea per se, so I can take the liberty of not citing the source. But this needs to be understood according to the circumstances.
For example, let’s say “love story” is one idea. If I write purely my own thoughts (my own intellectual creation) on this topic I need not acknowledge any one. But, if someone has written on this topic and I want to write about it (whether a commentary, or criticism, review or abstract) to bring it to the notice of others, then I must acknowledge it.
As per Copyright Act, a fair dealing of copyrightable work for criticism or review is permissible. A fair dealing in my view, also involves acknowledging the original source.
There is no need to mention the source, once the wordings change?
The above answers this question too.
You can make it a policy that members write a short review of the news items and provide hyperlink to the main article.