The first thing I will say that a lot of people don't realize, is that rice will ultimately make your issue even worse. Rice absorbs moisture and will trap any existing moisture inside for much longer, so you should not be using this iPad, even if it's been days since putting it in rice. It sounds like the buttons have been shorted. What you need to do is remove the glass and LCD and use isopropyl alcohol to clean off any corrosion and dry any water left inside. Let it sit 24 hours before testing it, it could be damaged connectors, buttons, or parts on the board, there is no real way to tell without looking inside.
The only way around that is to put it in recovery mode and restore it using iTunes installed on a computer. It will erase the phone completely and you will need to know your Apple ID credentials to unlock the device.
Yes, only if you're willing to open up the device which is unfortunately the safest way to replace the glass without damaging the actual camera lenses. If part of the glass is already missing then there's no real need to open the device up. You'll want to chip it out along with the adhesive using a razorblade or a pair of tweezers. You can find the replacements online for a couple bucks. Just note that there is a possibility of the cameras being damaged already if any glass shards found their way to the actual lens.
