Is there a way I can access my IPhone Apps to maintain them from another IPhone or type of technology while waiting for a replacement Iphone due to hardware failure?

If I understand correctly, it sounds like you were unable to recover your iPhone’s prior backup during your first sync, although you should be able to update any iOS device using the same sync method hereafter. If you’re not able to get access to another iPhone hardware this week, I would suggest syncing up with an iPod touch as an alternative.

If your contacts and calendars are sync’d up (at least like they are on my Mac), you could use some combination of Skype and Google Voice to replace the call functions in place of your phone. That’s what I did when I lived in a dead zone at least…