The taps in question look to be quarter turn taps, so as such won't have a washer, but more likely ceamic tap valves. Replacements for these can be brought from any decent plumbers merchant and are very cheap. They come in pairs, as the hot and cold ones are different, ensure you fit the right one, although they are colour coded clue and red for ease.
To get the tap heads off, I believe there is a small allen grub screw on the rear of the heads.
No - the seat of CD taps doesn't wear because no water passes across it.
It's far more likely that you've fitted the wrong valve for this tap. Where did you get the replacement?
BTW, there are tens of different types of what look to be similar ceramic disc valve bodies, and very few merchants have enough stock to be able to supply them all. If you have an obscure one then you'd be best getting it from the original tap supplier.
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