Unsourced Profiles don't necessarily have a suggestion. To see suggestion of the profile you work on, you have to go in the column with the WikiTree-ID to the button "suggestions". If you "only" want to source a profile you click on a profile of the list, source it, remove the {{Unsourced}} template and save the changes. Then you go up to the green banner, click on the button "Challenge Tracker". New site opens. There you click on "Sourcerer's challenge" and add the sort of source you added (BMD; Census, whatever). In case there are other issues with the profile, the suggestions are also shown on this site.
And yes, Aleš updates the lists once a week. But if there is a profile e.g. born in England died in Australia and you only add sources that prove him in Australia and the England part of his life is still missing, the profile stays in the Unsourced list. And because there is in a location field "Australia" the profile will also stay in the Australian list, no matter if it has already sources for the Australian life.