iPhoto not responding El Capitan download

No, but they should be backed up anyway. Note that you’ll only be able to redownload it if you previously got iPhoto from or associated it with the Mac App Store.

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I have read elsewhere that I should delete and re-download the app, however I don't want to lose all my photos! Will my photos be lost if I do this??

Your photos are in the iPhoto Library and not in the iPhoto Application. Moving the iPhoto Application to the Trash will not delete the photos. Do not run an uninstaller.

But before you do this, check, if you have an iPhoto version that can be updated at all. Open the AppStore and look at your Purchases history. Sign in with the AppleID you used when you purchased iPhoto from the AppStore or set up your Mac with iPhoto preinstalled. The apps that you can reinstall are listed on the fourth tab of the AppStore. If iPhoto is not shown there, try to unhide it (Mac App Store: Hiding and unhiding purchases)

if you cannot make iPhoto visible in the Purchased items, iyou missed the window of opprtunity to update iPhoto to version 9.6.1. Then it will not be possible to update iPhoto. You can open your iPhoto Libraries in the new Photos for Mac application however. See this link on how your iPhoto libraries will be migrated: How Photos handles content and metadata from iPhoto and Aperture - Apple Support