"Fucked up" and any use of the word "fuck" is VERY vulgar and you shouldn't use it. "screwed up" (or messed up) is not vulgar and is acceptable anywhere, to say that you made a mistake or something isn't right. Look at this sentence with one of the original uses of screw : "He screwed up the paper and threw it in the fire" Here you can see it means to make something unusable, or to crumple, so you can say: "This computer is screwed up" (it's not working right) "I screwed up this cake, it tastes terrible." "I screwed up at work yesterday" "The bad weather screwed up my plans to go to the beach."

They mean the same, but "fuck up" is vulgar. Be careful where you use it.

It depends on how you want people to perceive you. If you want to appear rude or aggressive that is the right time to vulgar words. It also shows that you are not educated enough to know other words that you can use. Any time you swear or use vulgar expressions or bad words you take the risk that people will not like you and that you will offend them. It can also be illegal in many public places under part of the law called "disturbing the peace". Where I live a 15 year old middle-class white boy was arrested for swearing in Walmart last week. I honestly have no idea why so many people want to use bad words . Why do you want offend native speakers and give people from your own country a bad reputation? If you are with a group of your friends and you know they swear, and you want to be more like them, go ahead. If someone grabs you it the street if you yell "Fuck off!" it would be more likely to get everyone's attention and maybe you would be more likely get help to repel your attacker. The problem is learning a language is difficult, so id you practice using these bad words and then you forget where you are and whether it is appropriate you will get in trouble.