#1 - Every unit and cities have three levels of view ranges for detection of stealth units: land, air and naval, but they are very small, so you if you need a bigger stealth detection you should use sentry planes.
[Green] - Land
[Blue] - Naval
[Light BLue] - Air
#2 - If they are inside your stealth detection range you can see them, otherwise it will appear that your opponent is moving empty transports/air transports.
#3 - With stealth detection, you can find them by luck when moving your naval units or you can use sentry planes also, just pay attention because each (land, air and naval troops) needs a different distance to be detected.