Are these two questions rude or offensive in English: "Would you like to do something useful?" (referred to somenthing that needs to be done urgently) and "I will remember it" (said to a person but referred to an unpleaseant fact happened)
If something needs to be done urgently, it would be inappropriate to say, "Would you like to..." The phrase "Would you like to..." is a euphemistic way of asking someone to do something. You are not asking them if they want to or would like to do it. It has the ring of insincere or pretended courtesy. If you want someone to do something, then say, "Would you kindly do this?" Or "Please, can you do this quickly? It's urgent." The sentence "Would you like to do something useful" sounds as if you are saying, "Do something useful for a change," and that is offensive because it implies the person never does anything useful. If something needs to be done, idiomatically we would not call it doing something useful, which merely means it has usefulness, not that it is necessary. If something unpleasant happens and you tell the person whose fault you think it is, "I will remember this," or (more likely) "I won't forget this," it has the sound of a threat: I won't forget that you did this bad thing to me, and I will resent you for it or I will do something in revenge. If you are merely expressing in a neutral way (without blaming someone) that you found the incident unpleasant, you might say, "This will be hard to forget." Why would you tell a person that you won't forget their unpleasant act unless you mean to offend them?