How do I permanently delete free apps from my purchased apps to eliminate any future updates from those unwanted apps?

You can't. The Purchased List is a complete listing of all your downloaded Apps. You can't remove Apps from that list.

If you don't want update priompts for certain Apps remove them from your iPhone.

You should not be getting Update prompts for Apps that are not installed on your iPhone.

You can hide purchased apps in iTunes on your PC. That way it won't show up as Purchased but not on Phone anymore.

Mac App Store- Hiding and unhiding purchases

iTunes Store- Hiding and unhiding purchases

You cannot remove items from your list of purchases. That is simply a list of receipts kept by Apple for your account.

I have requests for purchased apps NOT on my iphone.
There are a great many that were purchased and do not want.
In spite of how it happened, how do I delete or hide the info
for the app wanting to be downloaded?

Thank you.

You cannot delete any pre-installed iOS app.

If there is No 'X' on any apps you have Downloaded...

then check in Restrictions... Settings > General > Restrictions > Deleting Apps = Off / On

Understanding Restrictions > http://support.apple.com/kb/HT4213