Whatever you do, DO NOT use mains cold and hot from your tank, IT WILL BE AN UNMITIGATED DISASTER.
They have to be at pretty much the same pressure for any sort of mixer to work well.
A 3 bar pump will also probably give you a load of trouble with a static head as low as yours. Reason - if you suck hard at the hot water tank, even using the best method which is an Essex flange, the product of the flow down the pipe which supplies the HW cyl and the resistance to that flow in the pipe, will give a pressure drop across its ends, especially if it's small like 22mm. 3 bar is 100 feet of suck. The water in your feed tank is how far above the side of the HW cyl where you'll take the HW off?? Probably 3-4 feet if it's on the same floor. So if the pressure drop in the supply pipe is more than 3-4 feet they you're sucking AIR down the vent pipe. No shower, bugered pump.
And I'm astonished that nobody has told you that you seriously DO NOT want to pump the supply to the WC. It'll bounce about with the pump flicking on and off and keep everyone in the building awake.
So there's some of the things you have to avoid. Do some more reading. There's loads online at the manufacturers' sites, and forums llike this and plumbingpages.com . But don't believe everything you read!