For the Week solid line, Drag out Start from the left to the Columns shelf. Change the field to represent Week(Start) from the drop down menu that appears by right clicking. You want the "Week Number" from the lower date options. Change this to Discrete and then move the field between Month(start) and Day(Start).
Next - right click on this field and select "Format"
from the format menu that now appears - be sure the right field is selected - week(start) and then select the little grid icon. See the "Column Divider" field, select "Level" and move this one level to the right. You will now have week level lines in bold.
I do not know of a way to get the scroll to date or marked date for today to work though. Have you made any progress on that front?
There isn't a way to make Tableau scroll down to a particular entry. However you can use Highlight Actions to make it easier for your user to find today. I've attached an example workbook, but you can see directions for how to create highlight actions here Highlight Actions
Hope this helps
example highlight today.twbx 2.4 MB