Gmail forward all email – respond as original receiver

There is no elegant solution but here is one that should do what you want:

1. Using your Google Apps account, create a secondary user: garbagecollection@mydomain.com
2. Set the catch-all (in Control Panel for domain, email settings) to go to garbagecollection@mydomain.com
3. Write a Google Apps Script which scans the inbox periodically (every 5 min?, daily?)
4. The script would:
   1. Automatically add new addresses to a control spreadsheet
   2. create a label for each new address in your main email account
   3. forward each email to your main account (if not black listed in spreadsheet)
   4. apply the label in your main account

It would work as follows:

You create registration specific email addresses such as firstname.lastname.amazon@mydomain.com because the garbagecollection@mydomain.com is a catch-all, it will accept any email. The script records all new addresses it in the spreadsheet. When you want to stop receiving email, you flag it in the spreadsheet and the script deletes the email rather than forwarding it.

I believe you want the deliveredto: search operator.

Gmail advanced search

deliveredto:

Search for messages within a particular email address in the Delivered-To line of the message header Example: deliveredto:username@gmail.com

Meaning: Any message with username@gmail.com in the Delivered-To: field of the message header (which can help you find messages forwarded from another account or ones sent to an alias).

You should be able to replace your to:me@school.edu filter with has the words: deliveredto:me@school.edu. That should catch mailing lists and such.