depends on what car and what engine, typically if your cruising on a freeway, you will be running at half RPM or at the most 3/4, but the lower RPM the better with that you get better gas mileage.
What can cause the RPM on a car to jump while driving is a problem with the transmission. It could be a problem with the gears in the transmission itself.
while driving the rpm gauge work perfect, when start accelerating the rpm can not exceed 3 with interruption in the engine
Many things can cause lag while driving at a low RPM but not at a high RPM even if it is not the vacuum hose disconnected from the EGR valve as it could be the fuel filter. It can also be the park plugs.
Loose belst Opp's that's belts
Gears slipping, such as sudden high RPM's and loss of power while driving. Failing to change gears at a certain RPM in an automatic.
while you are in park? That should be normal. While in gear or driving, no that isn't.
transmission is slipping
RPM varies with what gear you are in and what speed you are traveling at.
Erratic RPMs while driving or in park could be due to a faulty oxygen sensor. It is also possible that poor gas is being used.
Standard transmission?, the clutch is slipping, probably beyond adjustment, replacement necessary.
No, that is not normal. Should be around 2500 rpms.
Driving on lower RPM's will reward you with higher gas mileage in addition to putting less wear on the engine. So, low RPM will be cheaper in the long run.