For the date bit, that's quite easy using the [man]date/man and [man]strtotime/man functions:
echo 'Tomorrow is: ' . date('F jS Y', strtotime('tomorrow'));
As for processing a form, there's easy PHP tutorials out there that should give you the gist of that. If you can give us more specific details and examples of what you've tried, we'd be more than happy to fill in the gaps or point you in the right direction.
PHP templating can be more of a challenging task. There are pre-made templating systems out there; the only one I can think of off the top of my head is called Smarty.