There won't be a guarantee that you can claim on for the taps, just get them replaced. Unless you have a guarantee on parts used from when you bought the house. But if you did, you probably wouldn't be asking the question.
The bits in your water could be any number of things. Most likely there has been roadworks or similar in your area and bits will have come out of everyones taps who was affected by it.
Could be back syphonage, do you have an outside tap without check valve? Or does your shower head reach the water level in your bath?
Could be scale in your pipework - most likely if you're in a hard water area.
If the bits are only from this tap then it's likely to be corrosion coming from under the bubbled plating.
What colour are the bits?