Actually, piccolo didnt say not to use your eyes. If i remember correctly, he said to unfocus your eyes. Focusing on one particular area would make it impossible to see such quick movements.
Then they didnt know it either..only after seeing them..with there eye's they could take there conclusion that it wasn't Goku.<!-- / message -->
This too is kinda wrong. I think you tried to prove that they could see from far distances, but then you contradicted yourself. All Z warriors sense the chi of living beings. They also
recognize familiar chi. They weren't sure if it was goku or not because the chi was so different from before. Goku's chi is recognized by each of the Z warriors, but after he became a Super Saiya-jin, they didnt know what to expect from him. They used logic to try to figure out if the fighter was Goku or not. Basically, both sensing chi and their use of their eyes failed them in this scenario. They didnt know it was someone else until they viewed him from a fairly close distance. Oh, and saiyans sense movement very quickly (fast eyes i guess) and piccolo can hear things from a mile away. This is what enabled them to identify the golden fighter.
Back on topic: As i said before, having sniper vision while using beams would make for some unfair combat. Theoretically, you can fight someone from the opposite corner of the map while using this sniper vision. Obviously, this wouldnt be fun for those of us who would prefer not be killed by a cowardly sniper.....unless playing a fps game in which i would take the role of a sniper (thats ok cause guns generally arent meant for close combat).