No, it doesn't appear that you can repurpose an old 24" iMac as a screen for your Mac Mini. The iMac only has Firewire and USB connections, which won't allow your Mini to truly make use of the built-in screen in the iMac. See this Apple discussion for more info: https://discussions.apple.com/message/59... Newer iMacs allow this, through the thunderbolt connection, but not the older computers...
Check out the instructions for opening the iPhone 5 here: iPhone 5 LCD and Digitizer Replacement There are several steps you'll need to do before completely removing the screen, As the above guide notes in Step 5, "Do not try to completely remove the front panel assembly from the rear case, as there are several ribbon cables still attached at the top of the iPhone."
If the proximity sensor still isn't working, you may need to replace the power button and sensor. While you've got it open you may want to replace the vibrator with a brand new one. iFixit has them for only $9.95
The iPod Touch 4G uses Toshiba NAND flash drive memory for data storage, and accessing this (by taking it out and putting it into a working iPod Touch, for example) is almost impossibly difficult. For more info you can check out the teardown, or perhaps this answer: Toshiba NAND Flash Memory - one or two chips?
According to Apple: "This may happen if the device unexpectedly disconnects during the update or restore or iTunes couldn't tell the device to go to the restore state." Check out the following page for suggested next steps (or you just might skip ahead to trying a different USB cable): http://support.apple.com/kb/TS5314