An expansion tank is needed on a section of closed line that is subject to variable pressure. The only sane cause I can discern for having two tanks in close proximity relates to multiple devices with multiple check valves or an undersized expansion tank. Whether that tank is before or after the water heater is usually irrelevant. The job is to take up liquid expansion between a closed faucet and a supply line check valve.
It may be the case that your water for radiators is separated from your drinking water. Two distinct systems with a check valve to prevent radiator water from draining back could explain a second tank.
I'd try to eliminate the flexible hose if at all possible. You can get a threaded piece of copper pipe and solder it into your plumbing system if you have copper plumbing.
In a well designed system, all of the hoses, valves, etc should exceed the threshold for the TPR valve on the hot water heater. So maybe the hose you had in there wasn't rated for enough pressure, or your TPR valve isn't functioning (very dangerous, you should test it).
For the tank itself, don't worry about water coming out of it. It will work just fine without water in it (in fact, it will likely work better since you've increased the volume of air absorbing pressure fluctuations). To pressurize it, you have to remove all water pressure first (shutoff the water supply and open a faucet) and then pressurize it with a pump up to your water pressure PSI level. As long as the tank holds pressure with the water turned off, the bladder is still good, and you can reuse the same tank.
If you're worried about dirt in the water side of the tank, fill and drain it a few times to see if you can clean it out. Chunks of rubber will likely get stuck in an aerator or shower head which would need to be cleaned out, so better to do this now.
In terms of mounting, they can be mounted any direction. If mounted vertically on a fixed pipe (doesn't matter which end is up) then you don't even need support brackets.
Best Answer
Expansion tanks absorb excess pressure, they don't maintain system pressures.
I think what you're looking for is a pressure tank. While similar in design to an expansion tank, a pressure tank serves a different purpose and is typically much larger.
If installed properly, a pressure tank can help keep system pressure more stable during high demand. However, they do have limitations. Specifically if the high demand is prolonged, the tanks ability to maintain normal pressures will be reduced or lost completely.
Once the demand is reduced, the tank will refill, and the pressure will again be stabilized.