PandaUser it's nearly impossible to diagnose remotely, but as far as I can tell:
The original problem was a leak, which you were getting round by topping up the reservoir.
During one of these top-ups the reservoir was overfilled, and there was some spillage.
Now the pump is not operating at all.
My thoughts:
Changing the pump may just be a waste of money, as you can't really tell what (if anything) else has also failed.
Changing the car battery should have made no difference to the leak.
Have you been topping up with genuine Selespeed fluid (CS Speed fluid is the recommended fluid in the UK, and it's not cheap - up to £20/litre). Anything else will probably cause other seals to fail too. I have seen the results of someone using gearbox oil in the Dualogic reservoir, and it wasn't pretty. The actuator was pretty much trashed beyond repair.
In normal operation the pump is activated when the driver's door is opened, and then whenever it is needed to maintain sufficient pressure for the actuator to operate.
If the system is operating properly the amount of fluid in the reservoir should go down slightly when the pump starts, not up, as the accumulator fills with fluid. In total, the amount of fluid in the system is only about 600ml.
Any leak is bad news, and should be dealt with as soon as possible to avoid further damage. The actuator does not have much tolerance of grit or anything else which could get in during frequent top-ups. And the fluid is expensive!
It is possible that fluid has found its way into the motor, and it is also possible that disassembly, cleaning and reassembly could revive it, but I doubt it.
It is possible to replace the brushes in the motor, but this is generally only a good idea on motors which are otherwise perfect. Any contamination or signs of arcing inside the motor usually mean a replacement is the best option.
From your description, I suspect that the simplest option would be a refurbished actuator, or repair of your unit by someone who has the skills and the tools.
An Alfa Romeo independent would almost certainly be able to sort it out, but I don't know how common they are in Israel. In general, UK Fiat dealers and independents don't seem to do repairs on the actuator - they just replace as a unit.
Good luck with whatever you decide to do.