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For your first measure (Number started this week), simply drag Number of Records onto the viz.
For the second measure (Number ending this week), you want to compare the week number for the Start Time to week number for Close Time, and if they are the same, assign a value of 1. Drag this onto the viz and aggregate by COUNT.
For the third measure (Ongoing Items), you just want to count which items have a NULL Close Time. Right-click drag this onto the viz, and aggregate by COUNT:
It looks like I have a newer version of Tableau than you so I can't share my workbook, but here's a screenshot of the final result. Let me know if this isn't what you're looking for!