Limit Calendar Dates

That's not possible. We use the calendar library of joomla for that and it doesn't support that without a lot of coding and modifications. That's however an interesting request so we'll see if we can come up with a solution in the future, but for now, you won't be able to do it.

That's possible.

For the checkout, you need to edit the file "cart" of the view "checkout" via the menu Display->Views. There you will have to add some PHP code, like that:

switch(date('N')){
case '1':
//Monday
case '5':
//Friday
case '6':
//Saturday
case '7':
//Sunday
echo 'Expected Delivery Date: Thursday';
break;
case '2':
//Tuesday
echo 'Expected Delivery Date: Friday';
break;
case '3':
//Wednesday
echo 'Expected Delivery Date: Tuesday';
break;
case '4':
//Thursday
echo 'Expected Delivery Date: Wednesday';
break;

}

For the email notification, you should edit it via the menu "System->Emails" (Business edition only) and add something similar but change the first line by:
switch(date('N',$data->order_modified)){

To display the date, you can do like that:

$day = 60*60*24;
switch(date('N')){
case '1':
//Monday
$date = time() + $day*3;
break;
case '5':
//Friday
$date = time() + $day*6;
break;
case '6':
//Saturday
$date = time() + $day*5;
break;
case '7':
//Sunday
$date = time() + $day*4;
break;
case '2':
//Tuesday
$date = time() + $day*3;
break;
case '3':
//Wednesday
$date = time() + $day*6;
break;
case '4':
//Thursday
$date = time() + $day*6;
break;

}
echo date('F j, Y',$date);

for the email notification, you would have to replace also time() by $data->order_modified
The format can be changed following this:
www.php.net/manual/en/function.date.php