"would like" isn't a conditional construction by itself, it's a more polite version of "want". if you need 2nd conditional in your dialogue, then don't use would + perfect infinitive, it makes the conditional mixed, it should be "- If you gave me a 10% discount, I would buy this hat!" And your last example is 3rd conditional, you should use "like" there too: ""If he had given me a 10% discount, I would have bough this hat. But he didn't change the price."

Thank you, sir! "If you gave me a 10% discount, I would have liked to buy this hat!" does this sentence sound strange? How would you formulate it?

For the last part, "If he had given me a 10% discount, I woukd have bought the hat" 3rd cond. Woukd like to buy it is not really one of the conditionals.