Both are possible, but you'll have to write code to get this done.

- Add a date picker to your form and change its name to "date".
- Copy the isDay() function from
http://enterprise-solutions.swits.net/infopath/switch-day-sections-jscript-xdext
ensions.htm to your form's code.
- Add an OnValidate event for the "date" field to your form's code and then
add the following code to this event handler:

if (!isDay(5))
{
 var objDate = XDocument.DOM.selectSingleNode("//my:date");
 eventObj.ReportError(objDate, "Date must be a Friday", false);
 return;
}

This code will prevent the form to be submitted unless the day is a Friday
and will show a red field validation error border around the "date" field and
a tooltip with the text "Date must be a Friday" whenever the user hovers with
the mouse pointer over the "date" field.

For more information on OnValidate and ReportError see
http://msdn.microsoft.com/library/en-us/ipsdk/html/xdevtOnValidate_HV01021372.as
p?frame=true
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S.Y.M. Wong-A-Ton