You do not have to re-install WordPress, nor would you lose all of your work because your settings are saved to the database.
If you are having trouble with iFeature simply connect via FTP and remove the ifeature folder from the wp-content/themes folder. WordPress will default to TwentyEleven and you will be able to login.
As a note for anyone else that has this issue: 404 issues when attempting to save settings or publish pages is related to mod_security rules in place on your server. If you have access to your server via FTP or some other kind of online file browser, you can attempt to disable the mod_security rules yourself by adding the following to your .htaccess file:
# Turn off mod_security filtering.
If you are unable to edit this file or that does not work, you need to contact your hosting company and have them whitelist your domain in the mod_security config file. Most hosting companies are able to do this for their users.