I have no idea about using a DX as a monitor. I've read a couple of articles in the past where people have done that with one Kindle or another but I thought it was just to see if they could do it, not because they really wanted to use it. I'm not sure how practical that is but if you have some reason to want it it might be worth trying.
As for lasting a couple of years it's anybody's guess but offhand I don't know of any reason it wouldn't last that long. Having it plugged in all the time probably will shorten it's battery life but if the battery is decent to start with two years shouldn't be an issue. And if it's not a good battery it can be replaced.
I have a couple of old tablets with batteries that won't take a charge anymore. Both still worked okay if they were plugged in. I used the past tense because one developed other problems but the other is still usable plugged in. However, I had another tablet that when the battery finally got too bad simply wouldn't start anymore. It's anybody's guess what the Kindle will do.
I don't normally like to offer guesses as opinions but in this case I'm not sure anyone can give you anything but a guess.
Barry