1. You can take a look at this sample
which actually filters content items depending on the parent. The difference in your case is that you have to work with NewsItem.
2. To see the search on each page you should have SearchBox on your master page(template)
3. Please check MSDN
4)I cannot replicate such issues
5)You can use Widget Templates that is available inside Design tab of the backend. If you download the SDK you will have a zip with all templates of Sitefinity.
the Telerik team
Do you want to have your say when we set our development plans?
Do you want to know when a feature you care about is added or when a bug fixed?
Telerik Public Issue Tracking
system and vote to affect the priority of the items