Perhaps you can try using a Hidden Field and store a Date Hash Variable to its Default Value property.

In the Hash Variable KB, an example of detecting the current date and calculating one week ahead is: #date.DAY+7.dd-MM-yyyy#
(Adjust date format to Date Picker display format as needed)

Then in the Date Picker form element, in the Start Date Field ID property, point to the hidden field form element ID. This should do the trick 
Reference: Date Picker - Validation

As for disabling weekend or selected date(s), this should be achievable via JS script in Custom HTML.

Thank you Chris. But how to do the validation ya? 

Chris ... I want to restrict the date selection to 1 month (30 days) prior to the current date ... does this look correct?

#date.DAY-30.dd-MM-yyyy#   

Hi Bob,

It seems to be correct. Only way to know is to try it out!

After I posted this question, I found that it was indeed working correctly.  I just needed to adjust the format in that statement to the format in the date picker (MM/DD/YYYY) to MM-dd-yyyy ... when the two matched, my intended restriction was successful.