Here is iFixit’s guide for replacing the battery on your computer: MacBook Pro 15" Retina Display Mid 2012 Battery Replacement I haven’t performed this repair myself, but I believe it’s a bit of an ordeal to deal with all the glue, so I’d make sure that you have a decent amount of experience and comfort with repair before attempting it. Best of luck!
Yes, iFixit recommends this on most of their dual drive installation manuals. Here’s the product page for iFixit’s own SuperDrive adapter, and it lists your Mac Mini as being compatible: SATA Optical Drive USB Cable Don’t be discouraged by your computer only having USB 2, those transfer speeds are completely usable. I frequently boot MacOS off of flash drives on my 2009 white MacBook (which only has USB 2), and transfer all sorts of stuff on that computer. I can’t guarantee that that one on Amazon will work, it looks fine, although it looks like it says something about power problems with USB 2 computers. It might be worth it to look around for one that will definitely work with an older computer, or research with that one more.
If it turns on and works when connected running it through a second monitor, it sounds like the logic board isn’t the part that’s damaged. When you shine a light at the internal display, do you see anything being displayed, or is it completely black? It sounds like just the display is dead, which isn’t as bad as the logic board. It might be a good idea anyway to remove the logic board and look over it to make sure there isn’t any corrosion or other liquid damage on it before you use the computer more. Do you know how bad the liquid damage originally was or what happened to it?
Double check to make sure that your new RAM is the correct speed for your computer. Your Mac uses PC3-8500 RAM. You may have bought faster, newer RAM, such as PC3-12800. This RAM is technically backwards compatible with your computer, but it forces the bus to run at the faster speed, which it can't do. I'm having trouble finding the Apple support article about this, but it works like this: The bus can only run at the 1067 MHz speed of the RAM it was designed for. The computer will only run at the speed of the slowest RAM module installed. If you have PC3-8500 RAM in both slots, that's great, that's what the computer was designed for. But if you put PC3-12800 RAM in both of the slots, the bus will try to run at the speed of that faster RAM, which it can't do. With one slow RAM module in one slot, and one fast one in the other slot, the bus will run at the speed of the slower one, which it's supposed to, and then slow down the faster RAM so that it can also work (this is currently how I'm running my 2009...
You mentioning the fans running loud makes me think the computer could be overheating for some reason. Try downloading something like Macs Fan Control (https://www.crystalidea.com/macs-fan-control) and seeing if the computer is running unusually hot.
Not a complete iPad no. Although, you could probably purchase the individual parts and assemble them into a whole iPad, for a painfully high price. If you're asking about replacement parts, then yeah, they can be purchased for your iPad here: https://www.ifixit.com/Store/iPad/iPad-Air-2-Wi-Fi-Cellular