Hi Karen,
To answer your first question, yes, if you have labelled a DatePicker object "From Date" and then use reference this "Value from Screen" it will use the date that was entered in this object. You will have to identify in your Custom Button, which field you want this object to be applied to. Admittedly, from what you have said in this post, it sounds like you have done this, but I write this just to make sure we are on the same page. One suggestion would be to take a look at the actions in the Save button from the "Add/Edit Activity" section, in the stock "CRM_NewActivity" Screen (specifically action #53). If you have the "Field Services" app installed in your Method Account, you could also look at the WorkOrderList Screen, because it allows you to specific a date range as well.
Please take a look at these screens to see if they might offer some hints as to the issue you are having. If after this you still can't get this to work, please let me know and we can see what else we might be able to do.
-Ben