Can I jailbreak my way out of a passcode request?
No.
You will need to restore using iTunes. The iPad will completely be factory reset (meaning like it's fresh out of the box). Your personal data on the device will be lost but you can redownload all apps for free using the same Apple ID you bought them with. 

However you might run into some issues since the iPad 1 only runs iOS 5 and most apps require iOS 6 nowadays. Some might still be downloadable since Apple added a feature to support old iOS versions parallel (see http://9to5mac.com/2013/09/17/ios-app-store-now-allows-legacy-app-downloads-to-support-older-hardware-and-software/). However this will depend on the App Developer, so you might run into trouble getting some (probably a lot) of Apps back if they are not backed up to your computer.

Safari isn't an App that can be updated by itself, it comes with iOS, and the version depends on the iOS version.