10 failed passcode attempts

You will be locked out (you won't have the option of trying again ) & will have to restore using iTunes:

Forgot passcode for your iPhone, iPad, or iPod touch, or your device is disabled - Apple Support

So sorry but my info was for iOS 7 & above. I didn't realize you were on iOS 6.1.3.

How exactly is everything else working just fine if you can't get past the lock screen? Or are you talking about Restrictions?

As far as I know, you will need to restore your iPad back to factory settings & set up as a new device since restoring from backup would bring back the same issue.

Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support

Yes, it will. The restrictions passcode is in the backup. If you restore as new, that will remove the passcode, but if you restore the backup, that will just put the passcode that you do not know back on the phone and you will be in the same place, same problem. You have to restore as new to remove the passcode, then sync your content back manually.

Well, due to forgotten passcode device needs to be restored and setup as a new device. Suppose that you've backup, do not install it since, backup also including passwords.

If you ve iCloud account signed in device, check your contacts on icloud.com see if it's synced or not.

Besides, you can try to import photos/videos manually to PC if you connect device to PC before and tap on trust before. Otherwise, you can view the content before unlocking screen.