I am still learning the D200, are using the D80. The camera is second hand, if I set it to P mode (which I understand is auto mode) the shutter stays open.

SOURCE: Nikon D40 won't stay in remote mode

read manual ! you can change it up tp 15min.

Find in Custom Settings > "17 remote duration".
if it is not there change first in SETUP MENU>CSM/Setup menu from "simple" to "full"

SOURCE: Nikon D80

EXPLANATION.
1. The problem with 18-135 lens is because it make from plastic. Main problem from plastic is it can be reshaped after a few usage. When the shape ran out, the contact point will be defective. When the contact point didnt really touched, the processor cant send signal to lens to do autofocus (the lens focus using the lens motor, not the body). When u set to manual focus, the body doesnt need to instruct the lens to focus.
2. You are focusing something that is to near than the focal point.

SOLUTION.
1.Try cleaning the contact point on the lens. Then mount it back until the F showing up (F= aperture). This solution depend on your luck too. if the gap between to contact is so far, then it might happen back. Usually when u need it badly. haha
2. try to get more distance from your subject. Just keep press the shutter until the camera focus.

CONCLUSION
1.But new lens with metal mounting. It will last and durable.
2.Buy macro lens to close up. normal lens wont focus at short focal point!!~

SOURCE: Nikon DSL D80 with "r02" error

normally, just removing the lens and putting it again you solve the problem. F-- problem means "there's no lens attached !"

SOURCE: nikon 18-200 mm vr lens not auto focusing on my nikon d200

lets start with the basics, try hard reseting it and try again, if that doesnt work then
try upgrading your firmware (if possible on your camera) and if that doesnt work then it may be the lens, but dont forget to spend a few hours trying to find a option for it in the meny

SOURCE: Nikon D80, how do you turn off the r09, r11 and/or

The r09, r11 or r17 just tells you how many pictures you can shoot before the internal memory buffer is full. It's not an error message, and I don't think there's any way to turn it off.