Hello. "Like" (adverb) = as if; seem = 像 Example: "...像這些事情沒有發生的..."

"So listen, please just pretend like this is normal. This didn't happen, okay? " like = as if So listen, please just pretend as if this is normal. This didn't happen, okay? Something happened, and we want to ease the mind of the other person. Perhaps they said something bad, or broke something. We want to reassure them that it is ok and we forgive them. We want to get past that incident, so we will pretend that it didn't happen. It will be as if the event never took place.

Hello! Perhaps a better word to use than "like " would be "that"; "like" would be used as a verb "to like something" or as a preposition - "a bike like the one I had". "that" is the determiner referring to something or someone in this case "this" which is the situation in the sentence.