Your Transmission Fluid serves three purposes - lubricant, coolant, and hydraulic. The answer to the question depends on the scenario you are in when the fluid runs out. If a coolant line were to rupture and you had a sudden, massive fluid loss, you should be ok because with the sudden loss of fluid, you also had a sudden shutdown of the hydraulic system (no fluid, no hydraulics). Very few parts are moving at this point, including you. You would likely pull over to the side of the road and shift to park, at this point, the residual lubicant would have kept the seals from drying up and would have given enough time to shut the engine without suffering any damage. If you were able to coast for a good ways when this happened, there is a potential for damage to occur. Note that when you fix the hose and replace the fluid - you need to follow the total-fill specs instead of the typical fluid-change specs. If you had a slow leak and the transmission was allowed to operate with marginal fluid level over time, then there is a big chance for failure stemming from lack of coolant and lack of lubricant - if this is the type of fluid loss you are talking about, expect to payout.
The transmission will fail.
In the long run it can cause damages. Change it to the correct fluids. a.s.a.p.
If a person adds the wrong transmission fluid many things can happen. Some cars can continue to run, others will have problems and stall out or not provide a smooth ride.
If it is an automatic you'll thin out your transmission fluid and burn up your clutch packs and valve body if driven. If it's manual it can make your transmission run hotter and burn up your gears. You should flush it immediately.
If you over fill your transmission fluid, you might blow out the transmission seals. It is most likely that some fluid will overflow, but no damage will occur.
DEATH
It will hurt a truck with a standard transmission to let it run in neutral with no fluid. All vehicles, regardless of transmission type, need transmission fluid and oil to run correctly. Allowing a vehicle to run without the proper amount of fuel lubricating the engine will likely do a lot of damage.
Alot of transmission fluids are the same as power steering fluid so I wouldnt worry
The fluid level in a transmission will not change unless it leaks.
if you run out of transmission fluid yes because then your car couldn't run
You replace the radiator
The car will not move when you put it in gear.