When we create a list(contacts, tasks....) a webpart version is
automatically added in the webpart gallery so you can easily put it
in the homepage, but it is only available on the site where you
created it.

We were planning to create a webpart that gets a certain list from a
certain site (either from http:\\localserver\site or
http:\\OtherServer\site) and display its contents like an ordinary
webpart.

I know there's a web capture webpart but they don't like it. I tried
putting a Data View using Frontpage(finally they agreed to install it
in our server!), it works well and refreshes when there are changes
from the original list however it only shows the view and it doesn't
allow the user to add new tasks i.e. Also it only works with sites
that are created in the local server machine. Connecting to sites
from foreign servers does not show up the Lists.

Any help on how to do this?