We can estimate your current pressure if you know the vertical distance from your bathroom to the bottom of the water tank (you can use meters). Since the bathroom is on the top floor, the pressure is lower than if the bathroom was on the bottom floor.
For instance, say it is 2m from the bathroom sink to the roof and then say the tank bottom is 3m above the roof. When the tank is close to empty, the pressure is 5m of head (about 16ft). You get ~0.5psi per ft of head (little bit less, actually), so your current pressure would be ~16ft*0.5 = 8psi (quite low)
You can use actual distances to see what you get, but you probably won't be more than 8-10psi unless the tank is on a very tall tower.
Let's assume that 8psi is correct and let's say the new pressure is 70psi.
(70/8) = 8.75
sqrt(8.75) = 2.96
This means that the water will now flow about 3x faster, so you'll fill that bucket in 40 secs. This works out to 7.5 GPM.
Does this tank only feed these bathrooms or are there other houses/apartments that it connects to?
Typical plumbing size in the US is 3/4" (~1.9cm) as the main feed line. Then you might run 1/2" (~1.27cm) to each bathroom (1/2" hot line, 1/2" cold line).
For the pump, there are probably several options, but you would be best getting a pump in India or Europe. India and Europe use 240v, 50Hz electricity. USA is all 60Hz with most house voltages at 110v and some larger items (water heater, stove, etc.) use 220v. The US pumps often come in both 110v and 220v, but they are designed for 60Hz power and not 50Hz.
For the shower head, you'll also want to go with something from India or Europe as the US head might not fit the threads on your plumbing. The shower head design won't matter that much once you get the pressure up.
The only issue that I see is how the tank is filled. Is it rain water collection or is it pumped from someplace? Since you'll have better flow with the new system, you will go through the water a little bit faster unless you take shorter showers.