Most are in good shape (Trade Ex has some nice ones). I heard they shoot quite nicely and I aim at picking one up eventually.
I'm not completely familiar with the conversion process but it has something to do with the chamber and the breech end of the barrel. There are some pages online, if you look through google, where someone has cut open an action and taken pictures of the conversion process.
Stick with nice mild loads for 7.62 Nato and stay clear of .308 Winchester as the pressures of this round will more than likely blow the action. Aside from the modifications to the chamber, the rifles are in their original configuration for the most part. Usually the receiver is blued, versus being in the white originally, and "7.62 N" stamped on the rear bridge.
Remember, these rifles were made between 1895 and 1897 and they are not Mauser 98 style actions so be safe, think smart, and treat them well.
You can always have a gun smith look at the rifle and fire some test shots through it to make sure she is safe, should you have any doubt what so ever.