You are absolutely right.It's pretty rude to say “给我...”.“给我”does not means to give to me in this sentence,here it means to do something for me,but in an very impolite way.It's usually used when ordering somebody.你给我出去 means as exactly same as 'fuck off'.Same phrases like 你给我去死/Go hell! 你给我开门/You fucking open the door!

一般来说，这样说是不礼貌的。“给我”，我觉得更像是"following my order"的意思。

I believe this is classified as a "祈使句" (Imperative Sentence). There is no vulgarity about it whatsoever. It is simply a command "Get out!" If the listener doesn't expect to be commanded to leave, it may sound rude but certainly not vulgar. 祈使句主要用于提出请求，发出邀请，给予指示、忠告或警告，也可发出命令等。 source: 1) http://www.iciba.com/%E4%BD%A0%E7%BB%99%E6%88%91%E5%87%BA%E5%8E%BB 2) http://www.yygrammar.com/Article/201103/2031.html

“给我”---具体看放在什么句子和场合说，如果仅仅是这两个字“给我”，按语法来讲是正常的陈述句（дай мне）。但后面加上动词和具体的东西，就有点不礼貌了，一般表示愤怒和生气，属于祈使句(давай..,) 希望所说的能帮助你。

不同的适用情况。有时是不礼貌的，有是因为当时的说话人非常的愤怒(跟礼貌无关)。