To answer your previous question, the coil could perforate and lead to mixing of water. It happens rarely and is very unlikely to be anything to do with the system water quality, though maintenance will obviously help make it less likely still. If the header tank for the cylinder is higher than the header tank for the boiler, then you may indeed experience the water level rising as described in this thread.The problem still persist - water keeps rising and eventually overflows.
As i understand on a correctly working system this should not happen and the water level should(mostly) stay at 1/3 of the tank capacity.
There's no leak from the tank itself now (I suspect it was caused by the frozen overflow pipe but was not able to prove it) but there is still a problem of water rising to overflow level and discharge through overflow pipe even though the ball valve is replaced now.
I'm assuming you have two header tanks. If the cylinder feed cistern has been drained, then it is possible air could have got into the pipework to the taps. In theory they should be self-venting, but if there is poor pipework design, there should either be a manual vent somewhere, or you can try the old plumbers' trick of trying to backfeed the water through the affected taps using a garden hose to try to force the air to travel up the vent above the cylinder feed cistern. Or just run them a bit and the airlock will eventually clear itself as it sounds like there is a slight flow.Other issue I noticed is there is almost no hot water pressure and flow in the upstairs bathroom taps. The showers and baths are ok but they have water pumps installed hence they have been always fine. The taps, however, is a mystery to me.
I have contacted the plumber who replaced the ball valve and he said it would not have been caused by him. However, I have got almost no hot water pressure and flow in the upstairs bathroom taps since his visit.
Any ideas?
With regard to your earlier question about having to wait 45 seconds for water to your taps, a pump would reduce the time, but you'd still waste the same amount of water. Other solutions are a secondary return pump (look it up on a search engine image search for a diagrammatic explanation) or, as you suggest, a pressurised cylinder. Most of these solutions are quite expensive and if you actually want to reduce waste by increasing the pressure, you need to also have the pipe run made from narrower pipe.
If you're really lucky, you may find the system you had worked perfectly well in the past until someone decided to 'modernise' the house with taps that invariably don't give a very good flow with the few feet of pressure you most likely have. Old-fashioned taps that use washers and meeting the former BS2456 or BS1010 standards are still available (just about) and I have a bath tap of this kind giving me 22 litres/minute off around an 8 ft (standing) head of pressure. If you're unlucky, then the pipework will be creating resistance to flow, so changing the taps won't help very much. I suspect waiting 45 seconds for hot water, while far from ideal, is something most people will accept, so the installer may not have bothered trying to get this time down any lower.