(American English speaker here) 1) This is correct English, but it sounds a little formal. I would say, "Don't be offended. I didn't mean it." 2) As a cat owner, I would say, "hide" instead of "taking cover". So, you could say, "My cat likes hiding under a blanket and sleeping there all day long." You could also say "My cat likes to hide under a blanket and sleep there all day long." 3) I would replace "take pity on" with "feel bad for" and "a bad temper" with "bad tempers" (each parent has their own temper...), so, "I always feel bad for children who have parents with bad tempers." You can use "pity" or "take pity on", but both sound somewhat formal to me. 4) I believe your sentence is fine in British English. I would say, "Do you really put milk in your green tea?" 5) This sentence is fine. Although, "It was stupid" and "to rule out the option" belong to different registers. If this is an informal sentence, then maybe it would be better to say: "It was stupid to say they can't come at the same time."