Would an ipad 2 case fit an ipad 3rd gen?

It should fit. The iPad's 2,3, and 4 are all the same size. The only difference the iPad 4 had a narrow lightening connector instead of the wider 30 pin connector in the iPad 2 and 3.

Edit. My mistake. A little more checking shows the iPad 3 to be slightly thicker then the iPad 2. I doubt the same case will work.

Yes. Be sure to see my edit above. It appears you need a iPad 3 case. I'm not sure what you mean by iPad1 3rd generation. Go to settings> general> about> model and google the model number to be sure.

Yes

There's really no such thing as iPad 1 third gen

I'ts iPad (what became iPad 1 once the 2 came out)

iPad 2

iPad 3 (which was only sold less than a year)

iPad 4

iPad Air (5th gen)

iPad Air 2 (6th gen, although it's rarely referred to as such)

iPad 1, 2 and 3 are pretty much the same. (except for the thickness which I think was to accommodate a different battery) iPad 4 is where the lightning connector came into play. iPad Air and Air 2 had some major size changes.

Your case might fit, it all depends on what kind of case it is. If it's a close fitting silicone or hard case, then likely not. if it's a portfolio kind where you slide your iPad into a sleeve or space in a case then it might. Those are the most forgiving of cases and the extra couple of millimeters in thickness are usually able to slide by.

Depending on where you found the case, if the place has a good return policy you can always give it a try and return it if it doesn't work well.