Both.
No,it does not do any damage to the engine or the drive-train of the vehicle with an automatic transmission
The transmission is located in close proximity to the engine, usually (in Hyundai's) transversely mounted directly under and behind the engine (behind the engine in terms of: following from the front of the vehicle towards the rear of the vehicle). If you follow the transmission fluid dipstick housing (shaft) down - that transmission fluid dipstick housing will end directly into the upper-most part of the transmission housing.
The year, make, model, transmission and engine info would help but it is probably the transmission down shifting if the vehicle is an automatic.
If the vehicle is an automatic transmission then you will find a DIPSTICK inserted in a filler tube that goes down to the transmission . Locate the tranny in the engine bay and you will find it. It IS IN THE ENGINE COMPARTMENT and is very similar to the OIL dipstick but it IS LONGER. If the vehicle has a MANUAL (w/clutch) tranny then the only way to check it is from underneath the vehicle by unscrewing a drain or drain/fill plug. This is always on the SIDE of the transmission and looks like a HEX bolt.
Look in the engine compartment very carefully for the dipstick. On an engine mounted longitudinally, as in a RWD vehicle, it will be located near the firewall. On an engine mounted traversely as in a FWD vehicle it will be normally located on the drivers side down low in near the transmission, but it may be on the passenger side. On some newer vehicles, especially GM, there will be no dipstick as the transmission is a sealed unit with no way for the owner to check the fluid level.
As you are looking into the engine bay from the front the transmission is on the back side of the engine about half way down.
The location of the dipstick for checking the transmission fluid varies from vehicle to vehicle. For vehicles with engines mounted in line with the drive shaft and transmission (pickup trucks, Ford Mustang, Chevy Camaro, ect.) the dipstick for checking the transmission fluid is usually located near the back end of the engine block, sometimes lower down along the side of the engine. It often looks like the dipstick that used to check the oil. Remember to check transmission fluid the engine should be running when your doing it. Also its important that you don't over fill.
Yes coasting downhill will save you fuel. However do not do this with a vehicle equipped with automatic transmission. You will damage the automatic transmission by coasting. You can do this with a manual transmission but do not shut the engine off. This would cause you to loose power steering and power brakes.
the two sensors on a transmission communicate with the computer to the engine and tells the transmission when to shift up or down....
to pull the vehicle down the road using different gears. if you didn't have one, then you could only go as fast as your engine revolutions allow. Also without a torque-converter your engine would stall when you stopped the car.
The output shaft speed sensor is located behind the engine on top of the transmission case under a tin cover on the mid-passenger side of the vehicle it's difficult to see from under the vehicle but that is the only way to get to it. There can be as many as 6 speed sensors on that vehicle. If you have anti-lock brakes, there are 4 speed sensors(one at each wheel) for the anti-lock brakes. There is a TSS(turbine speed sensor) on the body of the transmission toward the driver's side, and there is a VSS(vehicle speed sensor) on the output shaft housing of the transmission on the passenger's side down behind the engine, where the passenger's drive shaft plugs into the transmission, on the topside of the transmission case. in the transmission
The starter on a 1996-98 BMW 740il is located on the right side of the vehicle under the engine down by the transmission. Opening the hood will allow you to see the the starter from the passengers side of the vehicle.