How do I allow registration for one day of a multi-day event?
I have successfully used price sets for exactly that purpose. 

You can customise the event confirmation/receipt at Mailings > Message Templates > System Workflow Messages.   These are written using Smarty.

{if $event.id  eq 'XX'} will let you selectively customise the receipts for a particular event.

{if $line.label eq 'Friday only'} should let you customise at the individual line item level once you are in the line item loop.

For scheduled reminders you may be able to use Search Builder to create smart groups based on the fee label and so send different reminders depending on the day(s) of attendance using "Limit to - Group ".